Why “Catch-22,” not “Catch-19”? The only people who know the answer to that question would be the author, Joseph Heller and one of his publishers, Candida Donadio. There are no regulations or manuals for all the “Catches” in the military at the time, or any after that. It seems that they were just made-up phrases by the soldiers (or by Heller) to describe the redundancy of the tasks they had to perform.
Heller was originally going to title the book “Catch-18,” a term for what Yosarian, the main character of the book, was doing at the beginning of the book. His job was to censor letters from the soldiers to friends and family back home, blocking out passages that the military though too “sensitive” for them to see. The catch was that whoever censored the letters had to sign his name on the correspondence that he censored, making it known to that he knew what was in them, but they didn’t. To get back at the authorities that had him do this, he would make up names to sign on them.
The soon-to-be publishers didn’t like that title, since it would clash with a book coming out by a well-known author, Leon Uris. That book was titled “Mila 18.” Heller and the publishers came up with “Catch-11,” but the new Frank Sinatra movie coming out was called “Ocean’s Eleven.” Heller then suggested “Catch-14,” but the publishers didn’t like that.
Eventually, one of the publishers, Candida Donadio, came up with “Catch-22.” The rumor is that October 22nd was her birthday, but she said in her phone call to Heller, “I’ve got the perfect number. 22, it’s funnier than 18.” Why it’s funnier than 18 we’ll never know.
I believe the origin of the "22" refers to a situation in the cardgame blackjack, in which the goal is to reach a sum of 21 by adding your card numbers and faces. You add to your hand's total by drawing cards blind. If you go over, (that is, 22 or over) you bust, and lose. I am not overly familiar with the game, so I cannot be anymore specific than that without making something up.