Its fascinating how the anti-AA types always manage to abstract the 400 years of white male advantaging, that forced us as a society to arrive at this point. Where they do that at? One only needs to look at the economic distribution between whites and blacks to put a period on the sentence of an AA debate.
That said, let me try and add another dimension to the discussion. Because of our overall economic distribution trends of the last 30 or so years, where wealth has concentrated at the top and constricted for the population at large, white privilege carries far less social and economic capital than it did, say, even, 15 years ago. As a country we now have roughly 80% of the population fighting for less than 25% of the wealth. Like mos def said, its simple mathematics, and it adds up to a whole lot of folks being left a$$ out.
So for a lot of cats, no matter how well-intentioned, white privilege naturally falls on deaf ears. But therein lies the rub --- while the 1% gave marching orders to the middle class to wage war on AA, religion, unions, regulation, etc they used that misdirection to extract our wealth and refashion our set of principles and ideas. Our current socio-political environment is the result of that work.