The phrase 'Catch 22' comes from the book of the same name by Joseph Heller. Today we often use it to describe a no-win situation like in your example. http://en.wikipedia.org/wiki/Catch-22_(logic)

Yes. Your example is a catch 22 situation. http://en.wikipedia.org/wiki/Catch-22_%28logic%29#Real-life_examples

I think you can't use this idiom this way . "a catch 22 situatian " is to describe one get in two situatians,which is difficult to choose which one do first.

The Catch 22 paradox is presented as the trap that confined members of the US Air Force in the novel of the same name. In logical terms the 'catch' was that, by applying for exemption from highly dangerous bombing missions on the grounds of insanity, the applicant proved himself to be sane (after all, that's what any sane person would do). If anyone applied to fly they would be considered insane. Either way; sane or insane, they were sent on the missions. This might be described logically as, 'damned if you do and damned if you don't', 'the vicious circle', 'a chicken and egg situation', or 'heads I win, tails you lose'.

两难推理