You're deeply mistaken if you think there aren't men who don't genuinely prefer the traditional order of women being subjugated by men.
1. Not everybody shares your values.
2. People who don't share your values are not necessarily brainwashed.
3. People may do things that are irrational under your system of values, but rational under their own.
And BTW, there is no a single fighting force in the world that doesn't have old men persuading young men to sign up and risk throwing away their lives. There's not a whole lot of difference between regular soldiers persuaded to participate in a forlorn hope or banzai charge attacking a defended position and a suicide bomber or kamikaze.
The 'traditional order of society' is a society run by psycho pathological individuals and benefits nobody except for those individuals.
But you already knew that, didn't you?