Implication of unstated contrasting cases

The entirely correct conclusion drawn in the question is a result of a phenomenon detailed first by the philosopher Paul Grice. The rules he formulated for what he called "Cooperative Communication" are known in linguistic pragmatics as Grice's Maxims.

One of them says we should make cooperative communications true, as far as we know. Another says we should make them as complete as possible. The upshot is that, when one says something less than what is logically possible, one possible reason is always that that's as far as one can go and stay completely truthful.

This is known as a "conversational implicature" (a name picked by Grice so as not to be the same as "implication", which is a different logical animal). There are many words and constructions that have special Gricean meanings, like the difference between try doing it and try to do it.

In the example sentence, if it were the case that no one could become priests (or be made priest, or however one phrased it), then one could say so. And in that case it would certainly be trivially true that no woman (and no man) could become a priest. But if less than that is said, the extra unsaid racist, sexist, etc proposition (this is the way that stuff works, folks -- subliminally), Men may become priests is conversationally implicated. (note: not "implied" -- "implicated", like a politician)

And if you only say

• Men may become priests.

without hanging a Gricean impicature on it by negation, you leave open the logical possibility that others (e.g, women, children, dogs, oysters) may also become priests.