catch 22

A catch-22 is a paradoxical situation from which there is no escape because of mutually conflicting conditions.

The term comes from Joseph Heller's 1961 novel of the same name, in which a military rule states that pilots can be grounded for insanity, but requesting to be grounded proves sanity—so no one can ever escape combat duty.

The phrase now applies to any no-win dilemma where the rules themselves prevent a solution: It's a catch-22: you need experience to get hired, but you can't get experience without being hired.