from the title of Joseph Heller's 1961 novel. In widespread use only after release of the movie based on the book in 1970. The "catch" is that a bomber pilot is insane if he flies combat missions without asking to be relieved from duty, and is thus eligible to be relieved from duty. But if he asks to be relieved from duty, that means he's sane and has to keep flying.
See catch (n.).