All feminism wants more than equal rights. Feminism is not about equality and never has been, it is about increasing the social mobility of women. One of the very first feminist victories is widely regarded as the Tender Years Doctrine, a legal victory which forbids men from getting full custody of children during a divorce, it's been slanted since day one. That's why the vast majority of dudes in the movement are not domineering alpha chads.
I'm not in any way involved in this, but from what I've witnessed most of them are shy nerds and as close as a man could conceivably get to the non-threatening non-masculine feminized ideal many of these women have and they find themselves still in their crosshairs, and they just rightly ascertained that there is no egalitarian endgame even in discussion.
That's just it. It's opposing views over what is equal. It's not about male domination or female domination, it's opposing stances on how much ground should be given on either side in order to achieve equality. Neither side argues "I want male supremacy" or "i want female supremacy," but rather there are legal scales that are nearly impossible to balance as you get closer and closer to actual equailty.
My favorite examples relate to abortion. Let's say that the man and the woman in these situations are both pro-choice
overall, and believe that a baby could be aborted for reasons that aren't strictly medically necessary, just to eliminate that from the proceedings.
Situation 1 is Tyrone the Kingpin. Tyrone has committed enough crimes to earn him a life sentence, but has yet to be caught. In order to achieve something that will be very difficult for him to do behind bars, he quickly finds a young wife and promises that she can depend on him financially to raise a child. She cannot afford this kid alone. He knocks her up, then gets arrested and all his assets are seized.
In a society where the mother needs the consent of the father in order to abort, he will never give her permission. Does she have the right to abort?
Situation 2 is Latoya the Destitute. Latoya cannot provide for herself, but she's hot, so she finds a man for whom she can bear his kids and depend on him. However, she's clever, so she finds someone wealthy, then abandons him as soon as she gets a positive pregnancy test, then explains that she expects childcare payments.
In a society where the father needs the consent of the mother in order to abort, she will never agree to abort. Can he abort her child?
Both sexes want to win the overall advantage over abortion. They wanna win. But it doesn't make them sex supremacists.
An actual sex supremacist would be more along the incel line of "Every man has the right to a woman to impregnate in order to maintain his mental health," or "the state should subsidize prostitution" or whatever.