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Single word or phrase for "something that can be done and also cannot be done for some reason"
For example a job that you hate and you don't want to continue but also you can't leave because you need a job.Or something that you ate, you don't want to spit because you like it somehow and don't want to swallow because you dislike it.
The circumstances OP describes are often termed a "catch-22" or a "double-bind."
catch-22 noun: a dilemma or difficult circumstance from which there is no escape because of mutually conflicting or dependent conditions. "a catch-22 situation"
synonyms: dilemma, quandary, vicious circle; (Google)
double-bind noun: a situation in which a person is confronted with two irreconcilable demands or a choice between two undesirable courses of action. (Google)
You stay with the job you hate because it's impractical to do otherwise. On that job, you don't insult your boss by telling him what you think of him because it would be impolitic to do so. There are probably as many adjectives as there are reasons for refraining from doing something not barred by the laws of physics. These solutions may be in general called only theoretical because though possible, you are constrained from implementing them in reality.
If you're of two opposite minds about something, then you're ambivalent about it.
In your examples, it seems that you're stuck and whatever you do next will be a bad move. You can call it a
no-win situation/lose-lose situation
a situation in which a favorable outcome is impossible; you are bound to lose whatever you do (TFD)
You can also use the chess term zugzwang
Zugzwang (German for "compulsion to move", pronounced [ˈtsuːktsvaŋ]) is a situation found in chess and other games wherein one player is put at a disadvantage because they must make a move when they would prefer to pass and not to move. The fact that the player is compelled to move means that his position will become significantly weaker. A player is said to be "in zugzwang" when any possible move will worsen his position.
(Wikipedia)
This is a bit esoteric, but the best fit IMO, since it denotes the compulsion to make a move when you rather wouldn't.
Or a Cornelian dilemma
A Cornelian dilemma (dilemme cornélien) (also spelt in translation with two "l"'s i.e. "Corneillian") is a dilemma in which someone is obliged to choose between two courses of action either of which will have a detrimental effect on themselves or on someone near to them. In classical drama, this will typically involve the protagonist experiencing an inner conflict that forces them to choose between love and honour or inclination and duty.
(Wikipedia)
