According to standard grammar, “they” and its related forms can only agree with plural antecedents. But English sorely lacks a gender-neutral singular third-person pronoun, and “they” has for centuries been pressed into service for that purpose, much to the grammarians’ chagrin.
When pressed on whether “they” could serve as a singular pronoun, my fellow lexicographers and I pointed out that it already has done so for about seven centuries, appearing in the work of writers from Chaucer to Shakespeare to Jane Austen.
Merriam-Webster associate editor Emily Brewster turned the question back to the audience. The only thing standing in the way of singular “they” becoming more acceptable? Copy editors who take it upon themselves to edit out the usage, she said. ...
Dozens of gender-neutral pronouns have been put forth over the years, including “thon,” “xe” and “ze,” but all have failed to catch fire. “They” has the virtue of actually being in common use, and even grammatical sticklers may be coming around to it.
--Ben Zimmer, WSJ, on cracks in the wall