Catch-22

 "Between a rock and a hard place", in other words - there is no way out/solution because of the conflicting rules or pressures one is facing.

• It's a real Catch-22: to get a job you need experience, but to get experience you need a job.
• John would be hurt if she didn't invite him, but if she did, Mary wouldn't come. It was a Catch-22

Catch-22 is a satirical novel by the American author Joseph Heller.  It is about a pilot in the Second World War. It is frequently cited as one of the greatest literary works of the twentieth century.

The phrase "Catch-22" has entered the English language, referring to a type of unsolvable logic puzzle.