(originally from something written up for a class)
In matters of fine distinctions, when the terms used in the discussion are themselves matters of contention, a definition must be supplied in order to ensure it is, in fact, the same idea being discussed. The terms here are "love", "God", "permission", "bad thing", "innocence", and "person".
Love is the will for the good of another. This includes both the wish and the pursuit of that good, though sometimes only the wish is possible. What is the good of another is that which allows the other to most fully be what and who they are. Because all persons share the "what" (human nature), we all share some goods (food, water, clothing, loving care, etc), but because each person is a unique "who", there are also unique goods which may apply to some persons and not to others (that particular job, this specific house, knowing that specific thing on the test, etc.). So there is a general love for humanity and a specific love of persons. Love, being an act of will regarding the good as abstracted most fully, is an act only rational beings can perform, as reason is that faculty which allows a being to most fully abstract a quality from the material, sensory inputs from which the idea springs. Further, to love is an act in one's own interest as well, because a person as "I" is defined in contradistinction to a "You". And if a person is necessarily only able to self-conceptualize with reference to another, the other is a necessary part of the self, because that other makes the self to be who it is. To summarize, love is identification of oneself with another and the rational desire that they be the best other person they can be.
God, most truly, is beyond words, being something like the Tao of Lao-Tzu, the pre-rational foundation for reason. But as the cause of all things, God is also, as though by analogy, the maximal Being. In this sense, God is Good Itself, Truth Itself, Beauty Itself, Life Itself, perfect Unity and Infinitude. By virtue of the Unity of the Being of God, so also is the Act of God singular--the bestowal of being on all created things. This single act has a different effect on all beings, as the shining sun has a different effect on wax, clay, grapes, and solar panels, not because it differs in act, but because the objects of the act differ in potentialities. It can also be seen that such a singluar Act is capable of the formation of a diversity of such objects of its continued Act when one considers the Big Bang cosmological theory, by which it is said that a single point of energy burst forth and gave rise to the universe in which we presently find ourselves. The two might even be one and the same Act--but this is another matter. In any case, God is also perfect Mind. This is clear because God is posited to be the creator of all material things, thus being Itself Immaterial (often called "Spiritual" in contrast; this is also the reason it is Timeless/"Eternal"), and the only immaterial reality we seem to encounter with causal powers in the world is the human mind. Further, the Act of God is to sustain the being of all created things as the things they are. To do this implies that God has, in some way, the form or nature of all things within Itself, since the cause of something seems to contain, even if not in exactly the same way, the effect in itself, as fire heats things because it is hot and the pen writes because it has ink in it and I speak words because I have internal words (thoughts). And the only immaterial reality we encounter that has forms or natures of things in itself is the human mind. Finally, because there are truths which would remain true even if all living things were to die suddenly, there must be a Mind to contemplate these truths. If a tree falls in the woods, you better believe it makes a sound no matter if someone hears it. A triangle with a right angle in it will still have sides related to each other according to the Pythagorean Theorem regardless of if no human is around to know that. But to say "the relationship between sides holds true in the things themselves" does not answer this objection which intends to show that God is a Mind, because the existence of the relationships is not the sames as the propositions being true--as they are--and this status of "truth" applied to a proposition is a claim about the relation of an abstracted relationship, not the relation of the things in themselves (since no physical triangle is actually perfect according to mathematical proportions). Therfore, God is a Mind which created all things and sustains their existence by a single Act, being the perfect and One archetype of all good qualities. (As an extra note, it is this trinity of Existence, Form, and Act which seems to parallel the NeoPlatonic One, Mind, and Soul, as well as the Christian Being [Father], Word [Son], and Will [Spirit].)
Permission is the absence of action by the one permitting when an action could be taken by them to prevent the action they are permitting. Applied specifically to a rational being, this is to deliberately not intervene.
By "bad things", we can mean a great number of different groups of things. There are unpleasant things (things which appear to be lacking some good quality), obstacles (things which prevent us from acquiring something with good qualities), and things which cause harm (removing good qualities from ourselves). Further, the term "bad things" can refer to acts. For this topic, we can collapse acts and beings into one analysis. Among the three categories of bad things, not all seem equal, and many seem mixed. Getting a vaccination seems good, but not to the baby who receives it. Vegetables are good, but not in the mind of the child made to eat them. Study is good, but not to the college kid who wants to do something more fun. Etc. In all these cases, there are mixed qualities, but it seems the greater weight is to be placed on the good. This implies that goods which allow us to become more fully what we are (medicine to prevent disease killing us, food to keep us healthy and active, and education to allow us to act wisely and make things) outweigh the bad qualities we endure to have them (pain, bad taste, inability to go out with friends sometimes). Sometimes, though not even close to always, we find a kind of goodness even in the bad qualities of what we have to endure, like enjoying the burn from a workout, being satisfied with a paper all the more because of the effort put into it, or laughing over a campfire about some stupid thing you did when you were younger to impress someone you liked--that worked. We recognize the bad quality of all these things, the pain, the inability, the hard work, the embarassment, etc., but they seem allowable, expected, and reasonable. They are "worth it", and are seen as the only way to be able to have to good thing we want. After all, if you want to be up in a tree or at the top of a mountain, you have to climb or have someone or something do so for you. But there are bad things which are not like that. Serious illness, death, abuse, starvation, shaming, etc. These are not worth it, and seem to have no such value. Further, there are some goods like human life and dignity which seem to be without "greater good", at least among human concerns. And this is why the atrocities of genocide and other unspeakable things are not tolerable even for some "greater good" of genetic purity, national economic standing, etc. And the reason is apparent when considered in light of the previous statement: "goods which allow us to become more fully what we are outweigh the bad qualities we endure to have them". It makes no sense to have a good above the personal well-being, since it is the goal of all action, itself. Therefore a truly bad thing is something which would prevent a person from becoming their best self.
Innocence is a term meaning lack of culpability in performing some bad thing. To be culpable is to be owed a punishment. What is "owing" is what we expect to occur, as in "you ought to pay your debts [given societal morals and possible consequences]" or "it ought to rain today [since it usually rains every so often and hasn't in a while, and especially since the weatherman said it would]". A punishment is some bad thing (not necessarily a "bad-thing" as defined above) that comes upon someone as a result of their action, as in "he was punished by hanging [because he killed the sheriff]" or "the road punished that boarder [because he didn't wear a helmet and isn't very good at skating]". Though usually we mean a punishment to be something inflicted by a rational agent. So innocence is a state in which one would expect nothing bad to happen to the person as a result of their behavior. More specified to the context of societal enforcement, this would mean that innocence is a state of being in which a person has not acted in a way warranting punishment.
Person has been defined above (and again here more clearly) as a rational being living in relation to another such being.
So restated, we are asking: "How can a Mind which created all things and sustains their existence by a single Act, being the perfect and One archetype of all good qualities, identifying Itself with other rational beings, and desiring that they be the best other persons they can be, deliberately not intervene when something which would prevent them from becoming their best selves happens to them, when their actions have not warranted punishment?"
To this, there may be several answers, some of which simply deny the question even is the right one to ask.
One, God's desire for our good may not be the only desire God has, and the other(s) might outweigh the desire for our good. This is often the view expressed in Reformed Churches, where the glory or fame of God is considered to be a higher priority.
Two, the desire for our good as persons may itself limit God, since to be a person is to be a rational agent, and to be rational is to have free will. Our having free will would then be something God would be unwilling to compromise, similar to the genocide example above; it would be destroying the very reason for doing it. Further, to love requires a free act of will, and this seems central to this will for our own personal flourishing that God has.
(Note also that since God is that which sustains the being of all things, Itself perfect Being and Good, and our own greatest good is to be most what we are, we seem to be saying that complete being and perfect good are in some way equivalent. These equivalent qualities, being and good (and some people include unity, beauty, thing-ness, etc.) are called "metaphysical transcendentals" or "convertibles", and by "converting" the one into the other in our statement about God's sustaining all things in being, we can say that since the principle act of a rational being is "to freely will", and good is convertible with being, God "freely wills the good of all things"; that, you'll note, is equivalent, per the above definition, with saying, "God loves all things". God wishes we all become the best selves we can be, simply because that is the nature of God, to love.)
Then we begin to consider the ways in which the question can have some part denied. I'll only examine single parts being denied at a time.
Three, one could deny that there is a God. But then one can't blame God any more than they can the Berenstein Bears for the evil in the world. And it seems I've met more than a few people who blame Someone they claim they don't believe exists to be blamed. But I've also met some who have genuinely not blamed either God or the Bears for the evils of the world.
Four, one could deny the definition of God given above. But that would take a very long time to refute in the myriad ways it could be denied. So I'm not going to go there.
(Further note the self-identification of God with humans seemingly hints at a God-becoming-human-ing, which is, of course, the doctrine of the Incarnation.)
Five, one could deny the definition of love given. But the competing defintions would seem to be physical desire, friendship, familiarity, and sacrifice. Physical desire might be an effect of love at times, but often it is a symptom of something quite separate. Friendship seems to be usually among equals. While this is possible if the Incarnation is accepted, God in Itself is radically unlike humanity in every way. Further, non-equal friendship seems to be based on common pursuit of something, whether business or sport or something else. But here I have already shown God to be in common pursuit with us of our own becoming our best self, and so in this way, friendship with God is possible, and already included. Familiarity is largely treated in what was said of friendship, and this seems to have its primary basis among humans in biological similarity, something again impossible to share with God unless some kind of an Incarnation is believed to have taken place, and further, that in the context of a human family, with whom He might be similar and familiar. Finally, sacrifice seems to mean giving up some good for the sake of the good of another. But God is Good unto Itself. So this is impossible. However, were there to be, as has been mentioned several times now, a radical self-identification with humanity in the form of an Incarnation, then there could be, both really in physical terms, and analogically by participation in the Incarnate Person, divine terms, some kind of Sacrifice for mankind. But of course, this is the doctrine of Kenosis and the Crucifixion, and possibly the Eucharist, depending on the denomination.
(I do not mean to use only Christian examples of groups with such beliefs, it's just that I know considerably more about them than I do of Buddhist, Hindu, Muslim, or other religious groups' beliefs)
Six, one could deny the lack of intervention is deliberate, and posit it is unintentional. But that seems to imply some kind of weakness or obstacle to God. And if the obstacle is not in God (as a greater will mentioned above) or in the things God created (human free will, also mentioned above), then it implies something else has power God cannot or will not overcome. This could be said to be an evil rational being of some non-human kind (like the devil), or some force (like chaos), but not some other God of the same kind as we posited, since there cannot be two "Greatest and Unequaled" beings; whatever would make them different would be a defect. And if we keep the God we have mentioned so far the same, then only the newly-posited "god" would have defects, and thus be utterly deficient compared to the One God. Further, the rational obstacle (devil) is a creature, and could be done away with or moved elsewhere more easily than we flick an ant away, and the force (chaos) is not truly a thing, but a non-thing; the absence of order. And how is God to fight absence except by filling all things with Itself? (Though human minds seem to be their own universes, in a sense, and it seems God requires human permission to enter before God is able to fill the human mind. This, of course, is reminiscent of many saying about faith, prayer, and purification through ascetic discipline and works. But this is basically the free-will thing from "Two".)
Seven, one could deny there are really obstacles that prevent people from ultimately becoming their best selves. This is effectively universalism, as it implies also that therefore all people really do become, eventually, those best selves. I hope this is true. One might argue that the objection doesn't necessarily require all to eventually become their best selves, only that they not be prevented from doing so. This can be taken two ways. One is to say then that our own will is the "bad thing", the obstacle, but this is hardly a line of reasoning that can be followed long, since it leads to denial of free will, and with it, rationality and personhood and humanity. The other is to say that those who, in the end, end up in a bad state of affairs, being always something less than their best self, tormented by the nagging conscience and perfection of those who do reach such a pinnacle of personhood, are only those who choose such a thing, and thus that it is a power given to us by God to become the little gods of our own minds and lock God out if we wish. (Since God is the sustainer of being, and thus to fail to become our most complete self is to incompletely allow God into our own self.) This is, again, the argument of "Two", above.
Eight, one could say God is justified in allowing bad things because we deserve them. No one, such an objector would say, is innocent in the way claimed. This seems flatly absurd, since it makes God considerably less merciful (which seems to be a part of loving) than most people, and altogether unjust towards infants. Further, while some bad things may be for our correction, if not all things lead us to ultimate correction of self into our best self, either "Sixth" of "Seventh", above, is true; namely that regardless of the justice of punishments God may or may not allow, either all are ultimately made into their best self (in which case all punishments were merely corrective to get us there) or else the punishments are not universally therapeutic, and some remain locked into themselves. Some might say that God actually wills to punish us for what we have done, but this seems entirely contradictory to the claim inherent in the question that God desires we become our best selves, especially if the punishment is done with no purpose toward that goal. Otherwise, it is a competing will, as in "One", above.
In summary (taking out the "dead end" choices), God may have higher priorities, be unable to stop our actions from having consequences if we are free, or actually end up making us all our best selves so it's "worth it".
While most deny the last option (and some question whether it can even make sense to say we have free will--which means we don't have to necessarily choose anything--and yet we all necessarily choose to become our best self, evenetually), and the first option seems inscrutable, because there could seemingly be myriad competing "wills" in God, and we might never know them, or at least this is imagined to be so (though it seems that if God's one Act is to sustain all beings, which is to say God loves all beings, then it is not at all apparent how from that same on Act some other, radically different will could be drived...), many find the second option appealing. Yet there are further objections.
Why, if free human actions are the causes of bad things, doesn't God prevent them? (Let's imagine for right now that natural disasters are the result of past human actions or other rational beings' actions.) There are four potential ways God could do so, and all can be ruled out in turn.
First, God could stop the cause in the person before they act. But this would be to remove our own free will and self-control of our minds, making us non-persons, but rather, robots.
Second, God could stop the effect from the person. Imagine ridicule comes out as silence from the mouth of some angry person, or a knife simply vanishes from the would-be-attacker's hands. The laws of nature have now become utterly unpredicable. Rather than inspiring change, it would probably unimaginably confuse us, since people make a lot of mistakes on a daily basis, all of which may contribute to the demise of others in some way, however obscurely and remotely. It took humanity long enough to understand the world to the level we do now, which is still incomplete--we never would discover laws of nature if they were constantly being broken. And one might say, "but God could invent or have the same effect as the life-saving things we have now to make up for that problem". But that almost would make us each in our own little bubble of God's protection and puppeteering, incapable of being a person, much less a human in a physical body, in any meaningful way. This seems like a rather pyrrhic victory.
Third, God could stop the cause in the victim, but this would basically be again to bubble us in, and presents all the same problems. Further, if God has one Act to sustain all beings, God would have to "change the Act" constantly, affecting everything wildly--something which seems impossible or hardly worthy of the Eternal, Perfect Creator.
Fourth and finally, God could prevent the effect of the bad action in us from, well, being bad. But again, this would be manipulation of our thoughts unless it was voluntary. But if it's voluntary, then God isn't totally able to prevent the bad things altogether, which is what's being discussed.
So, in summary:
I posit that God made us free beings, and wants us to become our best selves, but due to human actions, often very bad things happen to people. God permits this, then, because He has "tied His own hands", so to speak, in choosing to make us. Though I hope it turns out we all become our best selves, someday.