Nobody seriously runs an argument against the existence of God from trivial evils, like hangnails or mosquito bites.
Why not? Here is a hypothesis. There are so very many possible much greater goods—goods qualitatively and not just quantitatively much greter—that it would be easy to suppose that God’s permitting the trivial evil could promote or enhance one of these goods to a degree sufficient to yield justification.
On the other hand, if we think of horrendous evils, like the torture of children, it is difficult to think of much greater goods. Maybe with difficulty we can come up with one or two possibilities, but not enough to make it easy to suppose a justification for God’s permission of the evil in terms of the goods.
However, if God exists, we would expect there to be an unbounded upward qualitative hierarchy of possible finite goods. God is infinitely good, and finite goods are participations in God, so we would expect a hierarchy of qualitatively greater and greater types of good that reflect God’s infinite goodness better and better.
So if God exists, we would expect there to be unknown possible finite
goods that are related to the known horrendous evils in something like
the proportion in which the known great finite goods are related to the
known trivial evils. Thus, if God exists, there very likely is
an upward hierarchy of possible goods to which the horrendous evils of
this life stand like a mosquito bite to the courage of a Socrates. If we
believe in this hierarchy of goods, then it seems we should be no more
impressed by the atheological evidential force of horrendous evils than
the ordinary person is by the atheological evidential force of trivial
evils.
There is, however, a difference between the cases. Many great ordinary goods that dwarf trivial evils, like the courage of a Socrates, are known to us. Few if any finite goods that dwarf horrendous evils are known to us. Nonetheless, if theism is true, it is very likely that such goods are possible. And since the argument from evil is addressed against the theist, it seems fair for the theist to invoke that hierarchy.
Moreover, we might ask whether our ignorance of goods higher up in the hierarchy of goods beyond the ordinary goods is not itself evidence against the existence of such goods. Here, I think the answer is that it is very little evidence. We would expect any particular finite being to be able to recognize only a finite number of types of good, and thus the fact that there are only a finite number of goods that we recognize is very little evidence against the hypothesis of the upward hierarchy of goods.