Sarcasm is an adjusted stress reaction.

I actually had Mai on my list of ladies I wanted to do for the fest, but I'm glad you did it because you did it much better than I would have. (Them being the "cool kids" is really an argument someone uses? ZUKO?)

I've always sort of liked the idea that Mai was the deadpan snarker, who adopted that persona early on and the younger Azula sort of looked up to her/admired her and their friendship was built on that early on (because the girl who cares so fiercely about what her father thinks and impressing him and outdoing her brother, maybe she'd secretly envy someone who seems to NOT care about those things?), and then as Azula grew up and into being *Azula* the dynamics of their relationship changed. But that's not supported by any other canon than my brain.