Well, argue it with hundreds of years of English usage.
The Oxford English Dictionary traces singular they back to 1375, where it appears in the medieval romance William and the Werewolf. Except for the old-style language of that poem, its use of singular they to refer to an unnamed person seems very modern.
.....The well-respected Chicago Manual of Style still rejects singular they for formal writing, and just the other day a teacher told me that he still corrects students who use everyone … their in their papers.....