Glen shows us again why he is an economist and not a poet in this post on “You're So Vain,” inspired by Tyler's exhumation of the perennial mystery. (This page is entertainingly un-useful for the “who is it about” question.)
On my intepretation, which is, of course, the natural and correct interpretation, “You're so vain, you probably think this song is about you” is a self-indictment, expressing frustration and emotional paradox.
Carly, or whoever the implied narrator is, obviously can't get the guy out of her dome. She wants to hate him because he was just as aware of his allure as she was, which was irresistable, which is why she fell for him and he “had her.” She was thrown when he dumped her. And she tries to console herself by pointing out how vain he is. But, it turns out, his vanity is really just a fair acknowledgement of his overwhelmingly attractive qualities, a form of confidence and self-possession that is itself attractive. And so pointing out his vanity is an implicit acknowledgement of everything she loved, and everything she grieves losing.
(By the way, people who go on and on about how great they are, like Quentin Tarantino and Phil Hellmuth, drive you crazy in a special way that only those who live up to their own ridiculous hype can.)
The fact that she's still thinking and writing songs about him and how goddamn beautiful/perfect/irresistable/vain he was “several years” after he “had her” substantiates his vanity (like his Lear jet and his horse “naturally” winning at Saratoga), which is maddening, and throws her right back into the cycle of love/resentment. He is in fact the kind of person people write songs about and can't forget. She wants to hate him for the fact that he knows it. But, no, that's just why she loved him. He's right. He's unforgettably terrific. If she could just forget him, she wouldn't be singing the song. But she can't, and the reason she's singing the song is precisely why fell so hard for him, and can't possibly get over the fact that he “gave away the things [he] loved and one of them was me.”