Apologies
Saying sorry doesn't mean the same thing to me that it does to many, I think. I don't wait for someone to apologize for something they did. I don't instantly forgive them as soon as they say “I'm sorry.”
To me, an apology isn't much more than a show of humility. It simply says, I fucked up, and I'm self-aware enough to realize it wasn't a good thing. It's the verbal bowing of the head, making yourself small, backing off of your aggression.
Otherwise when people insult me or do something to me I don't like, I don't view it as some wrong that needs to be “righted” with an act of contrition. I see it simply as a plain, rare moment of raw truth. As social creatures we mostly try not to hurt others around us, so when I or someone does hurt others, it says something very important about who they are as a person — something unobscured by the faces we put on to get along with others; something very blunt and honest.
It's my view that you can't stop people from doing these things (only they can stop them before they happen), and frankly there's nothing to “right” once they've done something I don't like. They're just being honest.
What it comes down to as the receiver of such a slight, is what you're willing to accept. Apology or not, damage is still done (even the apologizer knows this; all they can do is shrink). The real important question that you can ask yourself at any point after the damage has been done is: are you okay with that person being around you, now that they've bluntly shown you who they are? Do the benefits outweigh the negatives of someone like that? If you didn't delude yourself into thinking you could change them, and had to accept them just like this, are you okay with that?