It's the elementary school version of "I'm sorry you feel that way."
Saying “I’m sorry” is never easy, especially when your teacher makes you write an apology note to another student who totally deserved it. But it’s a hell of a lot easier if you qualify your apology so much that it actually merits an apology. “I’d like to start out by saying I did nothing wrong. I know this because I tried for a good thirty seconds to generate a modicum of sympathy for you and completely failed. In fact, you should probably be apologizing to me for putting me in the position of having to apologize. Whenever you're ready."