Why The White Sorority Doesn't Want Black Members

The last post came from Amren which had the following image. I didn't see it in the linked piece but I'm posting it here:

I want to draw the reader's attention to point one. Casting aside the "y'all racist" lets answer the question: There are 3 major "Black" Greek Letter Organizations to which African-American women can join. WHY would they want to join another type of non-academic organization (I purposely left out Scholar societies. Now I think this is a question best directed to black women (and men) who did not grow up in a predominantly black community and were likely one of the only black people in their elementary schools and therefore have developed tastes and affinities that skew heavily white. The Ghost is not your "average negro" by any means, but wouldn't have even CONSIDERED a non black organization to join. But having seen other people who grew up under very different circumstances, I can see how such a question would be puzzling in the least.