The one and only thing that selected me for this brutalising treatment was my sex. I am a man. In the work place, competition is for dollars instead of points or bodies. But it's competition nonetheless, socially and personally corrosive. And it's horrible.
Oppression is complex, and the way different oppressions interact is complex.
I agree with Mary that we need as subtle an understanding of it as we can get. So let's not leave the oppression of men out of the picture. Let's not allow it to distort or excuse other oppressions either. Instead let's figure out how to transform all oppressions. This is the false consciousness that Marx and others have written about.