1) Typically used to signify that speaker does not care whether their behavior emotionally upsets someone else.
2) The term could also be used to acknowledge that the speaker's behavior could upset someone, but the speaker stands by their behavior.
1) *Slaps book out of someone's hands* "Oh, you were reading that? Sorry Not Sorry."
2) In a cooking competition
"I saw her drop her dish on the floor. I could have helped her, but I'm running out of time. Sorry Not Sorry."
January 03, 2017