A catch-22 is not a situation in which both choices lead to undesirable outcomes. That is called a lose-lose or no-win situation. A catch-22 situation CAN be a lose-lose, but it could also be a win-win or win-lose.
A catch-22 situation is one in which the solution is impossible given the cyclic nature of the premises.
The logic is as follows:
1. If X, then Y and Z
2. If Y, then not Z
3. Not Y or not Z
4. Not Y and Z
5. Therefore, not X.
Many people use this logical terminology as commonplace vernacular while using it incorrectly and not understanding the origin.
1. If a person is excused from flying, that must be because he is both insane and requests an evaluation.
2. If a person is insane (I), he should not realize that he is, and would have no reason to request an evaluation.
3. Since an insane person would not request an evaluation, it follows that all people must either not be insane, or not request an evaluation.
4. Since all people must either not be insane, or not request an evaluation, it follows that no person is both insane and requests an evaluation.
5. Since a person may be excused from flying only if he is both insane and requests an evaluation, but no person can be both insane and request an evaluation, it (therefore) follows that no person can be excused from flying.
This is the logical argument and substituted form of a Catch-22.