In fact, to catch someone's eye is an idiom, not eyes. the question is not about everyone being singular or plural. There are actually two issues concerning this topic: The indefinite pronoun 'everyone' is a singular pronoun that takes a singular verb.examples:
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Should it be everyone's, everyones' or everyones? May i have everyone's attention,. Are the words everyone and everybody singular or plural?
The possessive of everyone is everyone's, in the same way the possessive of everybody is everybody's.
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. I have the following sentence: In my experience, the spelling checkers get confused by contractions. There is a comprehensive article on the topic on grammar girl:
What would be correct in this case and why? The expression commonly used in both the affirmative and negative. Your deduction, that not everybody's cup of tea means not to everyone's liking, is absolutely correct. An example would be it flew over everyone's heads, or it flew over everyone's head.

Everyone who is coming will receive a gift.
Would the noun following everyone's be plural? The possessive form is everyone's (the form everyones' is incorrect).example: Joe got everyone's attention and started to speak. The indefinite pronoun 'everyone' is a singular pronoun.

