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1.
When one is apologetic that they are not apologetic about a previous thing.

Often used by sorority girls.
My friends' boyfriends all think I'm prettier than them... Sorry I'm not sorry.
by SIUGREEKS April 03, 2011
 
2.
Commonly used Canadian phase, born out of the excessive usage of "sorry", this statement allows the user to conform with the sintax of apology, but indicate that he is, in fact, not sorry.

Often used in situations where an undue amount of judgement or prejudice is being applied. A simple, direct way to tell the person their feelings/thoughts/opinions aren't changing your mind and you will not apologize.
Sally: "is that wine? Are you drinking while pregnant!?!"

Jane: "it is wine and it is my choice, Sorry I'm Not Sorry."
by Sorryimnotsorry September 22, 2013