Example: David Gelernter's recent anti-feminist grammar prescriptivist rant
He-or-she'ing added so much ugly dead weight to the language that even the Establishment couldn't help noticing. So feminist authorities went back to the drawing board. Unsatisfied with having rammed their 80-ton 16-wheeler into the nimble sports-car of English style, they proceeded to shoot the legs out from under grammar--which collapsed in a heap after agreement between subject and pronoun was declared to be optional. "When an Anglican priest mounts the pulpit, they are about to address the congregation." How many of today's high school English teachers would mark this sentence wrong, or even "awkward"? (Show of hands? Not one?) Yet such sentences skreak like fingernails on a blackboard.
Language Log suggests that `they' is used as a bound variable -- it doesn't pick out any one person or particular group, but instead ranges over some set of people or some set of groups of people. `It' can work analogously, ranging over individual things as a variable rather than a temporary name for some one thing. `He' and `she', by contrast, are not variables. They're temporary names, and have to pick out some one person, with some one gender. (Note that the two examples -- mine and Gelernter's -- can both be read this way.)
Still not happy with what you might be tempted to call a crazy revisionist grammar of `they'? Shakespere used singular they, as did Jane Austen.