"Impossible choice" refers to a situation where there are two or more options to choose from, but none of them are satisfactory or acceptable, making it extremely difficult to make a decision. Full definition
Parent advocates need to be careful that they aren't asking their school districts to make impossible choices. (thelunchtray.com)
Among many other things, this movie is partially about the difficult and almost impossible choices that leaders have to make. (slashfilm.com)
The easier choice would mean giving up everything in the world; the other harder, if not impossible choice, fighting for everything that he values. (dailyfreebooks.com)