Merriam Webster calls pronouns like everyone, anyone, someone, and no one indefinite pronouns—not singular pronouns. Consider If anyone wants a drink, tell them to sit their asses down at the bar. We could be referring to someone of either gender, no one at all, one person, some people, or all of the people. That’s quite an array of possibilities. Though indefinite, these pronouns do take a singular verb. There are only two choices here: singular and plural. English used to have a dual inflection which referred exclusively to two entities. But there isn’t a form of agreement for “indefinite. Singular verb agreement, whose primary function is to predicate one entity, takes on the secondary function of predicating an indefinite number of entities.
The singularness of verb agreement doesn’t seem to interfere with the notion of indefiniteness possessed by our indefinite pronoun subjects. But which pronoun do we use to refer to our previously defined indefinite antecedents later in a sentence? Obviously we don’t have a ready-made one whose primary function is to refer to an indefinite pronoun. Once again some other pronoun, whose primary function— this bears repeating for emphasis: whose PRIMARY function—is to refer to either singular or plural antecedents, but will be conscripted into service to refer to indefinite antecedents.
Starting as early as the 13th century, well before the emergence of Early Modern English, primarily plural they has been used to refer to indefinite antecedents, and remains the most commonly used today, although its legitimacy has not been universally acknowledged.
Primarily masculine singular he was the choice of the grammarians and schoolmasters who followed the creed of 18th-century grammar author Bishop Robert Lowth, whose preference was for English to imitate Latin.
So we have had he and they competing for the job of the secondary function of indefinite pronoun for about the last two-hundred-and-fifty years now.
Let’s pause to note that the indefinite is a secondary, extended function for both pronouns. The main objection put forth by the opponents of they is that because it is primarily plural, it “can’t” be used as a singular pronoun (“can’t” is an odd choice of words for something that “can” and has been used continuously for over 700 years). Yet the same people are happy to extend a secondary genderless function to he, and are utterly silent on the extended use of you for the singular, plural, nominative, and oblique functions in the second person.
But there’s a problem with indefinite he that makes it unsuitable for the job, and which has led to a major decline in its use today: unlike genderless and plural they, he is semantically just too singular and way too masculine.
A lot of things have changed since Bishop Lowth published his little book of English grammar in 1762, and it’s time for some people to stop pretending they didn’t get the memo. Yes, anyone who doesn’t care for indefinite they is welcome to rewrite their sentences around it, but it is intellectualy disingenuous to keep suggesting that indefinite they is wrong.