The rule is that which requires pronouns to agree in case with the noun (or pronoun) it refers to. “All of the boys wore their coats.” Both all and their are plural, and all is well. But in “Everyone must wear their coats,” everyone is singular and their is plural; clearly wrong but very common in everyday use. Why?
Although words like everyone, everybody, and someone are technically singular, the obvious perception among many is that they refer to more than a single person. The other problem is the pronoun; if we say, “Everyone must wear his coat” we’ve solved the grammar problem, but we’re into the realm of political incorrectness, especially if everyone is referring to people of both sexes.
As a substitute for his some people will use his or her (perfectly acceptable though a bit bulky); others use the less satisfactory but correct his/her. (Many writers disdain the use of a slash, though you will see it in nearby articles in this issue.) The English might say “Everyone must wear one’s coat,” but the use of one’s for his or her sounds stilted and doesn’t work on these shores.
Another very easy solution is to forego the use of a singular noun in this circumstance; substitute it with a plural noun: “All must wear their coats.” All is plural, and the solution is elegant except that people in ordinary conversation will use everyone (or everybody) without thinking in a sentence, and when they arrive at the pronoun, it is too late.
All we can suggest is that you be aware. Without condoning the misuse of the singular pronoun, we do acknowledge the difficulty. If you are speaking to someone who does care about our Mother Tongue, however, he or she (there, that wasn’t too bad) will appreciate and make a minor note of the proper use. And perhaps you’ll get the job!
Passing Note: Yogi Berra has coined a number of wonderfully nonsensical phrases (“That place is so crowded, almost nobody goes there any more.”), and now he may have a rival. Boston Red Sox’ Manager Terry Francona, at a news conference before the sixth game of the League Championship game with the Sox, facing elimination by the Yankees, said, after winning two straight, “If we lose tonight, we’ll lose our momentum.” (Oh yes, luckily for the Sox and him, they maintained their momentum.)
— Ken Butera