Puzzling

I heard a new song on the radio today. It went a bit like this:

You're so vain
I bet you think this song is about you
You're so vain (so vain!)
I bet you think this song is about you
Don't you
Don't you

Ok, explain how this song is not about the person she's singing the song to. She expressly addresses them as 'you' and 'you're', and then she claims the song is not about them. It's a confusing song.

To be honest, it sounds like she's still REALLY hung up on whoever she's singing to. If she was singing this to me, I'd be like "yeah, it is about me, don't you know it, glad I had such an impact on you."