What would you think of me accidentally insulted someone's dead mom?
That's cruel. What caused you to accidentally insult someone's dead mom?
I never meant it to happen, I was just angry at the time
Well like you said it was accidental so go apologize if you offend the person. You obviously feel guilty about it so try to find inner peace by seeking forgiveness. Otherwise, the guilt might eat you up.
I'm not going to apologize since I'm the better person than most people since I'm always surrounded by total assholes
It does not make you a good person just because the other people are more awful. Apologize before the person doesn't want anything to do with you. He should understand since it was unintentional.