A nice example of the way singular they works was overlooked (like health care, the economy, and everything else in the past week of "racial politics") during the brouhaha over President Obama's press conference remarks about the arrest in Cambridge, Massachusetts of Professor Henry Louis Gates. Obama said:
. . . the Cambridge police acted stupidly in arresting somebody when there was already proof that they were in their own home.
Why would he use they and their, when the antecedent, somebody, is syntactically singular, and we actually know that the somebody he is talking about in this case was Professor Henry Louis Gates, who is male? Why did he not say proof that he was in his own home?
(By the way, when I write they in this post, in bold italics, I mean the word described by the dictionary entry for they — the word that has the inflected forms they, them, their, theirs, themselves, and occasionally themself. Likewise, by he I mean the item having the inflected forms he, him, his, and himself.)
The answer to the question of why Obama did not use he is that he knows intuitively that is not how things work in contemporary Standard English. Obama (like any native speaker) would certainly use he if the antecedent were a name: he would say The Cambridge police acted stupidly in arresting Professor Gates when there was already proof that he was in his own home. (The version with they would be grammatical but with a different meaning: The Cambridge police acted stupidly in arresting Professor Gates when there was already proof that they were in their own home, and that could only have the meaning — absurd in the present context — that the police officers in question shared a home and were provably in it at the time of the arrest.) But antecedents like somebody are different.
Obama was trying to make a general claim about the stupidity of arresting some person x when there was already proof that x was in x's own home. The x in this paraphrase is intended as what a logician would call a bound variable. The issue at hand is which pronoun to use when expressing the same content in English. Now, Obama wasn't intending to limit himself to the claim that arresting Professor Gates was stupid. Doubtless he would think that arresting Harvard president Drew Faust in her own home, if she got snippy after she had shown her driver's license, would also be stupid — unless she had clearly committed an arrestable crime. And in contemporary Standard English, with antecedents like somebody or everyone or any citizen, people typically use the pronoun they for "bound variable" meanings in this sort of syntactic situation.
Strunk and White baldly assert that this is an error. They simply say don't use they with syntactically singular antecedents like somebody. They don't give a reason; and it is pretty clear they didn't know anything much about the literary evidence that they has been grammatical and normal with singular antecedents for six or seven centuries. Strunk and White are just wrong about Standard English syntax, here as nearly everywhere else where they deal with grammar in their book The Elements of Style.
Of course, you have a perfect right to hold the opinion that they with a singular antecedent seems distasteful or ugly to you. In that case I would advise you not to use it. But don't call it a grammatical error, because it clearly isn't one, and never has been. Don't say that it betokens a breakdown in our ability to tell singular from plural, because it doesn't.
And don't allege that it generally introduces ambiguity, because it doesn't. There is (as usual wherever pronouns are found) an ambiguity in what Obama said: it would be linguistically possible to read they and their as referring to the police — or, for that matter, to some group of otherwise unidentified third parties such as the Spice Girls. But to pick up on either of those grammatical possibilities would be going for a crazy interpretation when a sensible one was available. Nobody listening to the president misunderstood him in this way, and none of the journalists writing about it (as far as I know) even mentioned either possibility. Everyone understood his they and their as corresponding to bound variables.
Obama is a fluent and excellent speaker of Standard English, and his grammatical ear (if not his political ear!) was spot-on perfect on this occasion. Singular they was the right pronoun to use in the context. If you talk about arresting a man when he's in his own home, you're talking about arrests of males; if you talk about arresting a woman when she's in her own home, you're talking about arrests of females; if you talk about arresting a man or woman when he or she is in his or her own home, you're talking like a badly written statute or contract. Obama intuitively understood how to avoid all three of those undesired outcomes.
[Language Log reader Michael Straight tells me he once heard a clip on NPR of George W. Bush talking about the need for a father to take care of "his or her children." That would be how someone might put it if they felt anxious about committing a sexist blunder but didn't have the good sense to use singular they. —GKP]