I had to laugh reading the exchange. You went in balls to the wall because you believed you were totally enlightened to the race/privilege issue and kudos to you for trying to get a handle on it.
The answer to your question, imo, is she was right.
I kept stumbling over the same thing that it seems you're stumbling over when I was trying to understand white privilege: you are thinking individually, and she's thinking collectively.
The bottom line for me is no matter what I've personally done to try to be part of the solution for inequality, I still walk around in a different world than people with dark skin. I'm waved through on many issues that they aren't. Not my fault, but evidence of privilege.
You and I, if I read you correctly, are thinking more in terms of complete across-the-board racial equality on a case-by-case basis, and she's thinking one race should be the complete focus because they never got a level playing field. Your first question pissed her off because of that schism in perspective.
Anyway, you seem to be open-minded and seeking, and it looks like you're headed in the right direction. Don't beat yourself up too bad, but use this woman's answers to learn a bit.
BTW, hope you're healing from your crazy experience with the culty guy.