pronouns - Why do people use "he/she" than "they"?

I often see in particular Americans use the words "he/she" (also sometimes "he or she") as a gender-neutral pronoun.

This is grammatically incorrect (the sentence "he/she" makes no grammatical sense), it's clumsy, it's long (two syllables), and, to be a bit pedantic, it doesn't even solve the problem of gender bias, because why is it "he/she" and not "she/he"?

On the other hand, we have the perfectly viable alternative of using "they". It's short, it's grammatically correct, it's completely neutral, it just works.

So why do so many speakers use the clumsy "he/she" rather than the elegant "they"?