Paul Bloomfield in Humility Is Not a Virtue (PDF) argues, as you might expect, that humility is not a virtue.
Part of his argument is that many of the virtue-ish things associated with humility are really matters of justice. This part of his argument fails miserably. For instance, one phrase associated with humility is 'having a just opinion of oneself'; Bloomfield argues that this is naturally seen as really an act of justice (as shown by the 'just' part of the phrase). But in reality all this shows is that humility is at least similar to justice, which is trivial, since all virtues have similarities to other virtues. In the traditional way of understanding justice, justice is not primarily or directly about oneself at all, but about paying one's debts (monetary or otherwise) so that equality is maintained. There is no sense in which 'having a just opinion of oneself' can be construed as literally a performance of this action. When we say things like 'humility involves having a just opinion of oneself', we are using justice as an analogy, not as a classification -- humility is like justice but applied to oneself (so could be called justice loosely), which justice (in the relevant sense of a specific virtue) is not. Of course, we can use 'justice' to mean something broader and more loosely than any specific virtue; we do so a lot. But precisely because of this we cannot assume that something pertains to the specific virtue of justice merely because we use justice-words for it. Bloomfield says if you replace 'humility' with 'justice' in common statements about humility that you get something that makes complete sense, but notably none of his examples show this if we are talking about justice as a specific virtue rather than justice as meaning any aspect of character that is justice-y in some way -- justice as a specific virtue, for instance, tells us nothing at all about what about ourselves we should or should not be proud of. Bloomfield's arguments on this point are merely showing that humility is plausibly in the family of virtues clustered around justice, not that justice is the real virtue we are talking about when we are talking about humility. This is all the more sure given that, when Bloomfield talks about justice here, he characterizes it as having to do with respect and self-respect, which is not a traditional account of justice; this merely confirms that he is actually talking about a virtue in the justice family that is not the one we usually call 'justice', but another one, which we often call 'humility'.
He has a further argument, focused on the notion of humility as 'owning limitations'; Bloomfield argues that 'owning one's limitations' requires appreciating one's strengths and competencies, and that if you put this together with 'owning one's limitations', you don't have humility. Thus humility would only be 'half a trait'. But this argument fails as well -- 'owning one's limitations' may require appreciating one's strengths and competencies, but owning limitations and appreciating strengths are simply not the same act, and therefore they could very well be done by distinct traits. Futher, virtues can break up into virtues ('integral parts' in the old terminology), and it is entirely possible for a virtue to be analyzable into other virtues as integral parts, where those sub-virtues need to be combined together to reach their full potential as virtues, despite always being distinguishable. People have proposed something like this with justice, taking it to be analyzable into the virtues of beneficence and nonmaleficence; the fact that these sub-virtues need to be put together in a fully integrated character does not change the fact that they are distinct, with different objects.
These failures are largely due to the fact that many modern theories of virtue have a flat and unsophisticated notion of how virtues can be related to each other. But not all theories of virtue are flat in this way, and in a more sophisticated account it becomes clear that neither of these lines of argument could actually prove what Bloomfield wants them to prove. (Bloomfield mentions other arguments briefly in passing, but they also are poorly suited for drawing such a conclusion; for instance, that humility is learned through mistakes and failure -- this is not necessarily true -- unlike other virtues which are not -- this is also not necessarily true, as we see with prudence -- or that humility is phenomenologically unpleasant -- this is not necessarily true -- unlike other virtues -- this is also not necessarily true, as we see with patience and fortitude.)
But there is a broader point that Bloomfield makes that is, I think, quite relevant. Bloomfield notes -- clumsily, but accurately -- that humility makes sense as a virtue in a theistic context. No matter how good you are, your good is derivative and infinitely far from the greatest good, the divine good, and so it becomes a virtue to recognize that your good, however good it may be, is a finite and derivative good. If we don't assume a theistic context, it becomes much less clear why humility would be a virtue. Modesty in the sense of not being boastful still would be, but humility is a much harder sell if there is no good that is far and away greater and more fundamental than your own excellence. Bloomfield argues that humility could be a 'corrective' in cases violating equality, but I would argue that this does not work, and Bloomfield would simply have done better to reject humility altogether. For one thing, as he characterizes humility, it simply can't act as a corrective in the way he suggests, because humility as he characterizes it is not concerned with equality but lowliness, and whatever else may be said about humility this surely has to be in some way right. Another issue is that it becomes unclear that there would be much use for it, since people are usually not treating others as equal because they have a reason to treat them as inferior, whether good or bad; once you take out a principle like 'We are all in the image of God' or 'We are all equal before the judgment seat of God', the sense in which we are ever actually equals in practical situations is attenuated at best. People think that the excellent athlete should have humility precisely because he is an excellent athlete; but this is precisely the point at which the excellent athlete is not equal to other people. In the theistic context it makes sense -- you recognize the inequality but recognize that it doesn't make you 'all that', because before God other things matter far more. But take that away and it's difficult to see how human equality (as opposed to say, equality of benefit in very narrowly defined exchanges) is not just a polite fiction; all of the alternatives to God, like reason, end up being quite abstract and removed from the practical features of this particular situation.
In any case, Bloomfield is right that whether humility is a virtue depends at least in part on whether God exists. If God exists, the reasons for thinking that humility is a virtue are quite considerable; if there is no God, they are at least very limited and perhaps nonexistent. This is not surprising; what counts as a virtue for human beings will depend on what human beings are, and whether God exists or not has fairly direct implications for how we should see ourselves.