A condescending and insincere apology offered before telling someone that he/she is wrong, usually instead of explaining why the person disagrees with the other party. Often accompanied by derisive laughter and/or mansplaining .
As a bonus, this makes people angry, allowing the Sorry But guy to claim that he can't listen anymore until they calm down.
Jane: I think Obama's doing a pretty good job, all things considered.
Bobby: (chuckle) Sorry, but you're wrong.
Tom: Dude, cut that out. Everyone thinks it's really annoying.
Bobby: Sorry, but I'm going to keep doing it anyway.