I think there are two reasons.
One is as has been stated here, that /pol/ is incredibly reactionary and as you said OP, they don't really think women should have their own opinions and should just fall in line. I can agree to an extent, but women are important and they do have a voice.
Don't forget that in times past influential men often listened to their wives or took what they had to say in consideration. That is the primary way women exercised political power before getting the right to vote and hold office. So, I guess my point is , is that there has never been a time where women truly did not hold any political power, it was just done through men. I guess perhaps the man was a mediating force, if his wife had a good idea he would say it, if she had a bad one he wouldn't repeat it.
I think that is why John Stuart Mil was a big proponent of women's rights. His wife was very educated and smart and so he would take what she said seriously.
I'm kind of going off on a tangent here, but basically you have a brain, you are smart, so feel free to use that brain. Women have primarily been teachers and educators of children for a long time.
My second thought is this. The type of man to spend most of his time posting on chan websites is almost definitely a beta. That's why there is so much talk of cuckoldry and the like. The men on this board have experienced that, they have been friendzoned and so forth numerous times. They see society for what is is precisely because many do not have high status, thus giving them the ability to understand what went wrong in their upbringing, usually by blaming media influences (think of how many people on these sites specifically come from families with a divorce for exampe).
The point being that many men kind of hate women here because they've been treated poorly by them or haven't been high status enough to be able to attract the women they want. This breed resentment. These men who were primarily raised by women, with little male influence, feel they were betrayed and lied to by women and that is why they are failures.
The truly socially succesful and alpha man most likely has enough things going on in his life that he does not resort to posting on a chan website. I've recently returned to the chans because my life is in shambles, but most of my friends grew out of it after high school once we had more important things to spend our time on.
So, in short, I don't think many of the posters on pol are wrong per se, but they have a variety of psychological factors which lead them to dislike women on a visceral level, while at the same time deeply longing for one.
Maybe I'm just projecting a bit here too.