I figured out how to describe a catch-22. It is a situation where a necessary condition for success is also a sufficient condition for failure. You have to ask (necessary condition) not to fly (success), but asking not to fly (sufficient condition ) proves you aren't crazy (failure), so you have to fly.
If you haven't read Catch-22, this probably makes no sense. But you have read Catch-22, haven't you? It's one of the two best novels of the second half of the 20th century, along with Invisible Man.