Catch-22 was termed by author Joseph Heller in the book of the same name, and represents a "paradoxical situation from which an individual cannot escape because of contradictory rules or limitations."
The term is introduced by the character Doc Daneeka, an army psychiatrist who invokes "Catch-22" to explain why any pilot requesting mental evaluation for insanity—hoping to be found not sane enough to fly and thereby escape dangerous missions—demonstrates his own sanity in creating the request and thus cannot be declared insane. This phrase also means a dilemma or difficult circumstance from which there is no escape because of mutually conflicting or dependent conditions.
Are there any examples of authors from any era of Latin expressing this idea? The closest thing I can think of that would have been expressed by Latin authors is a Pyrrhic Victory, but that isn't quite the same thing.
Edit: Perhaps something related to circular reasoning?
The problem of circular reasoning has been noted in Western philosophy at least as far back as the Pyrrhonist philosopher Agrippa who includes the problem of circular reasoning among his Five Tropes of Agrippa. The Pyrrhonist philosopher Sextus Empiricus described the problem of circular reasoning as "the reciprocal trope":
The reciprocal trope occurs when what ought to be confirmatory of the object under investigation needs to be made convincing by the object under investigation; then, being unable to take either in order to establish the other, we suspend judgement about both.