Same reason religion is believed. Cultural indoctrination.
A lot of men today lived through an age where women were treated far worse than they are today. They probably can't adjust now.

And, natural narcissism. I've met plenty of women who think they are superior to men; not that they don't have valid points, but I think they are too quick to assume gender alone makes a person better.

It's a wide-spread problem, really. I heard from my cousin about a deaf couple who had a child with partial hearing demanded the doctor destroy the eardrum of the child, because they believed their insular society to be superior to that of mean hearing people.
I think it's a subtle form of insanity, the belief in ones own superiority, but what are you going to do? It's the one thing no one will ever seek treatment for.

Is a matriarchal society the solution to our problems?
[psychologytoday.com]

Good question.

People whose brains have difficulty climbing out of the Limbic are attracted to predictability, repetition, security, and hierarchy. They’re not evil; just “differently evolved”.

Those values can be expressed through religious or secular tradition, but tradition is the key. It’s limbic.

It's cultural. Always has been. Women were seen as chattel, mere property for use not so long ago. TV gave us Ward Cleaver who "worked", but June Cleaver did not (though she did).
It's ingrained and pervasive. Maybe it has its roots in some Christian religious thoughts, but that's not the only place male dominance rears its ugly head.

Cognitive dissonance.