I already have a mother. It feels disrespectful to consider another person such.

[Even if it's her birth mother, even if she has slight memories of her which she can only assume is the Force's doing, it doesn't matter. Her parents are the Organas; they're all she could have wanted and more.]

It's not as if I don't know who she is now, but she's not my mother any more than Anakin is my father.

[Well, literally they are, yes, but they aren't who Leia considers her mother and father, and that's what matters more if you ask her.]