The logic known as Catch-22 is one of endlessly creative rationalization. It can take contradictory statements and reconcile them. It can make completely irrational statements sound logical. By taking a statement and inverting it, Catch-22 always defeats those who try to reason through it. It uses circular reasoning and, through this, dooms everyone involved. They can never escape its madness.
The logic of Catch-22 is self-contradictory and makes no sense, even in the context of the mad modern world.
Even though the logic of Catch-22 seems contradictory and irrational, it makes sense and can be applied logically in the world of the novel.