What impossible question do you have in mind? I’m making my impossible quiz.

I think an easy “impossible question” to make up is one that could be considered socially nuanced in which there's “more than one right answer”.

How many fingers does the human hand have? Four fingers and one thumb! (But, the thumb could be considered a finger-like appendage)
What month of the year has 28 days? All of them. (Or February, but that changes to 29 days on a leap year!).