The education system is in even worse shape than we thought.
Not ‘Catch-22 situation’. That means what Nametag said. More generally, a situation involving contradictory conditions attached to a desired aim, such that any attempt to achieve that aim is bound to fail.
Not ‘zugzwang’. This chess term refers to when Player A attempts to put Player B in difficulties, but B’s response puts A in even greater difficulties.
Not ‘conundrum’ (a puzzle or riddle) or ‘paradox’ (an apparent contradiction, either intriguing or puzzling in nature, which seems difficult to resolve).
Not ‘Hobson’s Choice’. This means a choice which is no choice at all, e.g. ‘You can have it in any colour you want so long as it’s black’.
Not ‘Gordian Knot’. This refers to an extremely difficult and seemingly intractable problem, of a kind that would take a long time to solve if it could be solved at all. There is also ‘to cut the Gordian Knot’, which refers to a brash action which renders the solving of the problem somewhat redundant (like simply cutting a rope with a sharp knife as opposed to bothering to untie the complicated knot).
Not ‘zero sum game’. This is a term from formal game playing theory. It refers to any game, or game strategy, which must necessarily produce a result where the scores for either side would produce zero if added together (e.g. team A can only get 5 points if team B end up with -5).
To be ‘on the horns of a dilemma’ is a good choice when used correctly, since it does mean to have to choose between two equally undesirable alternatives. However, many people these days simply use the phrase, or the word ‘dilemma’, to mean ‘a difficult choice’ or even just ‘a choice or decision’.
‘No-win scenario’ is good, and applicable, but smacks of military jargon.
To have to choose between ‘Scylla and Charybdis’ is also good for those with a classical taste. It’s from Homer’s Odyssey, and means to have to choose between two equally unwanted alternatives.
You’re welcome, don’t mention it.