Who hasn't heard (or said) something like "Everyone needs to take their shoes off!" or "No one has had their dinner yet!"?
In English, we struggle with pronouns. We have lovely gender-neutral plural pronouns, like "they," "their," and "them,"* but all of our singular pronouns are gendered (or 'it,' and who wants to be an it?).
To make matters even more complicated, we have indefinite pronouns, like "everyone," which seem to capture lots of people, but are actually singular ("everyone" means each and every one... one, singular).
So, when the subject of a sentence is "everyone" or "no one," which are both singular, the verbs and pronouns that go with those subjects should be singular also.
WRONG: Everyone needs to take their shoes off!