What would be correct in this case and why? Your deduction, that not everybody's cup of tea means not to everyone's liking, is absolutely correct. The indefinite pronoun 'everyone' is a singular pronoun that takes a singular verb.examples:
The possessive form is everyone's (the form everyones' is incorrect).example: May i have everyone's attention,. The indefinite pronoun 'everyone' is a singular pronoun.
An example would be it flew over everyone's heads, or it flew over everyone's head. In my experience, the spelling checkers get confused by contractions. Unless of course you’re a buddhist or a cat, in which case everyone has multiple lives and both would be correct, depending on context. In fact, to catch someone's eye is an idiom, not eyes. the question is not about everyone being singular or plural.
Are the words everyone and everybody singular or plural? The expression commonly used in both the affirmative and negative. Everyone who is coming will receive a gift. Would the noun following everyone's be plural?
The possessive of everyone is everyone's, in the same way the possessive of everybody is everybody's. Joe got everyone's attention and started to speak. Should it be everyone's, everyones' or everyones? There is a comprehensive article on the topic on grammar girl: