The root of white male privilege is in the simple historic condition that for millennia for most families, in order to stay afloat, women needed to stay home, run a household and rise children. It was the capitalism that brought indoor plumbing, electricity, refrigerators, washing machines and fast food; freeing women from the drudgery of everyday chores. If not capitalism, most likely you would not be writing your comment, because there would be no computers, you most likely would be an illiterate mother caring for a bunch of children with no future.
In other words, today the white male privilege is not the obstacle for ambitious smart women. It is an obstacle for people who see capitalism as the problem and socialism as the solution.