The narrator treats women in a similar fashion to how the white, rich, ruling men treated black people and other minorities. Invisible Man is a story that really calls to attention the inequality and discrimination that existed during the time of the novel's setting. While many readers might focus on the discrimination that the novel shows existing between blacks and whites, the narrator does give readers evidence that women are just as discriminated against.
The battle royal sequence is a good example. The goal of the gathering is to provide entertainment for the rich, white men. The black boys are there to be humiliated for no other reason than the viewing pleasure of the audience. The naked woman is there for the same reason. She is discriminated against because she is a woman, and the men believe that makes her equivalent to an object that they can control. It's why they put her on display, and it's why they believe that they can sexually grope her.
The story shows readers that the true ruling power comes from having three items. A person should be white, male, and rich. Being a black male doesn't help. Being a white woman doesn't help. The narrator shows that women, like other minorities, are pawns to be used and abused.
As the dancer flung herself about with a detached expression on her face, the men began reaching out to touch her. I could see their beefy fingers sink into her soft flesh . . . It was mad. Chairs went crashing, drinks were spilt, as they ran laughing and howling after her. They caught her just as she reached a door, raised her from the floor, and tossed her as college boys are tossed at a hazing, and above her red, fixed-smiling lips I saw the terror and disgust in her eyes, almost like my own terror and that which I saw in some of the other boys.