Aw, girl, I get this a lot, as well. Usually my response begins with, "Well, I'm sorry that you associate intellectualism with 'being white', but hey, that's on you." or in your case, "Damn, it's too bad that youuuuuuur blackness is defined by such unimportant things. Mine isn't."
...and top BOTH off with a smile.
I save the latter for when I'm really offended, though.
After coming from being the only black girl in a graduating class of 848 (and LOVING my alma mater) and then going to an HBCU, I got used to the "white girl" comments fast. Safely attribute it to other people not having diverse enough friends/neighborhoods/circles/cliques to respect your uniqueness, and believe in the phrase "The people who matter don't care, and the people who care, don't matter.".
That's what works for me NOW.
As for over-generalizing, of course "we" do. For me, it seems like a really deep connection to not being satisfied with where one is in life, and the more they see other people in that same place, the more comfortable they are.. thus shuning those who are different. I know that doesn't sound like it makes much sense, but I swear it makes sense in my head, LOL.