Something I have been thinking about, without much commitment on the matter. One of the peculiarities of atheistic arguments from evil is that they are by nature arguments that something does not exist because it morally ought not to exist, or can always be translated into forms in which they appear to make this kind of inference. This is not always explicitly brought out, but it's at least very difficult to find an argument that is not at least implicitly committed to a claim like "To be morally perfect, one ought not tolerate the existence of any evil" or "Completely good people ought to prevent any evils they can" or something similar, and in such a way that this does significant work for the argument. In an atheistic argument from evil, it is always the premise that God is wholly good, or morally perfect, or omnibenevolent, or what have you that does the primary work of generating an inconsistency or improbability given the existence of evil. And if you weaken the ought-claim in virtually any way (e.g., "To be morally perfect, one ought not tolerate evil unless one has a really, really, really, really good reason") it always causes serious problems for the argument. Thus the point that arguments from evil can generally be taken to conclude that something (e.g., morally perfect being tolerating evil) does not exist (perhaps even cannot exist) because it ought not to exist.
Likewise, it's very difficult to find any close analogues to this -- that is, it's difficult to find any commonly used arguments that have a similar structure, with a focus on what morally ought not to be the case. This is not to say that there are no arguments that move from some kind of 'ought not' or 'should not' to 'does not'; these are actually quite common, and tell us quite a bit about what we usually mean by 'ought' or 'should'. For instance, if I know how a machine is designed and how it was put together, I might rule out the possibility of some particular error happening because, given what I know, it shouldn't happen. Likewise, I might say that a physical theory says X ought not to happen, and conclude that therefore X does not happen. As I've noted before, 'oughts' tend to indicate what is necessary to have solutions to particular kinds of problems or answers to particular kinds of questions; this is at least part of what 'should' covers, as well, although we often also seem to take 'should' to cover any kind of expectation. Either way, they concern what should be taken as given for a problem or question, often (although not always) conditional on other things.
What seems rare, however, is for us ever to do this in moral situations. Perhaps examples might be found in dealing with moral heroes of various kinds, in which we would be inclined to dismiss that something was done because it would be an immoral thing to do? But I cannot think of any real-life examples, and looking in promising places has turned up nothing. The usual way it works in arguments from evil is we start with a claim or assumption that Any A ought to do B; then conclude that Any A does B; and then add (for some particular topic) Not-B and conclude Not-A (for that particular topic). A designation like 'morally perfect' is taken to imply that what ought to be done is done, at least when it applies. But these will all be limit cases, which we don't usually meet in real life. That would explain the rareness. And it makes at least preliminary sense that you would need something like a limit case -- deontic necessities don't usually imply anything about existence or nonexistence, so to get that you would need (1) an unusually strong deontic necessity or (2) another strong modality to 'mix' with the deontic necessity. Atheistic arguments from evil, while sometimes not very explicit about it, tend to use the latter approach, drawing on the metaphysical or alethic necessity of divine attributes.
