dilemma

noun

1. A circumstance in which a choice must be made between two or more alternatives that seem equally undesirable.

   “A strong dilemma in a desperate case! / To act with infamy, or quit the place.”

2. Any difficult circumstance or problem.
3. A type of syllogism of the form "if A is true then B is true; if C is true then D is true; either A or C is true; therefore either B or D is true".
4. (rhetoric)Offering to an opponent a choice between two (equally unfavorable) alternatives.