Ai was a bastard.
Not in the sense of being mean, mind you – no matter what Bumi or Lin might say. But she was the daughter of a married man, born to someone other than his wife.
...not that the Kyoshi islanders much cared about this. They saw things differently from the mainlanders.
It didn't matter that Sokka wasn't married to Suki. Kyoshi Warriors couldn't get married anyways.
So as far as Ai was concerned, Lin and Su Yin were her sisters. Fellow warriors, you could say.
Sisters stuck together, no matter what.
She taught them that.