I don't believe that to be true at all. I think that this way of thinking is a copout, and has been used to justify men's bad behavior without consequence, shame, or guilt, while simultaneously oppressing women, by keeping them in subordinate roles.
Contrary to popular belief, women have sexual desires too, and not for just one man, as men would love to believe. I do not believe my hormones make me want to nest with my faithful soul mate.
The thing is, that historically, men have made most of the rules and have set the cultural norms, without including women in the discussion. Men have withheld things, like basic human rights, voting rights, property ownership, access to education, etc, and have done everything they could to keep women out of public spaces and in the home throughout history, forcing women to become dependent on men for economic and physical survival.
The ramifications of this, have an enormous psychological effect on women.
The role of women has been culturally defined by men and forced onto them and enforced by numerous means. Making women, especially those with children, economically dependent them, is one. Psychologically and socially shaming them for any outward display of female sexuality and female expressed desires. This is done by pitting women against each other by dividing them into "good" or "bad", offering protection and safety to the former, and leaving the latter unprotected, thrown to the wolves to "get what she deserves" and demonized as a temptress, a vixen, a whore, slut, etc..
This kind of social conditioning, complete with positive and negative reinforcement, has had a grave impact on women, and has led them to repress or sacrafices their own needs, wants, and sexual desires, in favor of a man's.
Social conditioning tells women that it's bad for them to express them or to have them at all, and to openly admit to having them would put them at risk to be unprotected, and vulnerable to predatory men and left at a economic disadvantage.
Any of those reasons would cause vast numbers of women to seek out marraige as a means of protection and economic resourse. When a person becomes dependent on another for survival, they are at a disadvantage. They are essentially forced to comply with the wishes of whom they depend on, lest they get discarded by them.

Seems to me to be a plausible explination as to why women in our culture, throughout its history, have "wanted" to "nest" and be monogamous. I highly doubt, that if these social conditions never existed, that women would naturally want to be stuck with just one man.
Men on the other hand, have always done what they've wanted to and with whom. It's very easy to have an excuse for this, by claiming it's biology for men to want to screw anything with half a pulse. It's just a way to allow them to justify dehumanizing women and to avoid the vunerability of intimacy and human connection with them, which is a hallmark of humanity, seperating us from animals.

I totally agree with you that men and women act wildly different and that hormones can't be ignored, they aren't the only factor of course but hormonal make up drives people's behaviour much more than most are willing to admit.
obviously there is also the society into which you are born, what your education and religious training was like.
I say this because gender is one aspect of human behaviour but so is the conditions under which you live.
Self evidently you have more choices in life if you are very wealthy , such as where you choose to live and even down to how many kids you might have. If your parents are well off and supportive then chances are that you will have access to further education.
Even in a situation like my own where I was the cuckoo in the nest; my dad was a soldier for 15 years, then a local delivery driver , a milkman, factory worker and my mum was a cleaner.
I was the first person in my family to ever go to university and my dad was absent while my mum was very working class and very sexist, racist and badly educated.
I got a really good degree in Russian and German languages , came second in my entire year group but people who had much worse grades than I did got opportunities and had jobs arranged for them through their parents or friends of the family. I had my mum and my brother and my mum was a violent alcoholic.
It's a shame but it was all very well being clever but if you have always only ever been surviving then you need to get lucky and hope someone is gonna give you a chance.
I think now in retrospect that I was possibly undiagnosed with Aspberger's syndrome whereas I just thought I had PTSD and anxiety and depression and who wouldn't?
I was lucky because I am British and so the state has always stepped in and helped me with the cost of living but it's a shame as I should have done much better.
I am happy enough now because I am most likely the only local organic gardener who speaks 4 languages!!! Lol

My point is that I was extremely bright and driven and got to university despite my mother trying to stop me because girls should get married and have a part time job in a shop.

I have never married nor had kids. I've lived with a couple of boyfriends at different times but I was scared shitless that the violence she exhibited to my brother and I might be contagious and that I too might end up an abuser. I deliberately decided to stop the buck there and not have any kids just in case.

So my point is this - in a 'free Western society one ostensibly has free will however the way in which we are brutalized by the world when we are growing very much determines your personality type which in turn dictates your choices but my childhood paralysed me emotionally to such an extent that all of my life choices were coloured by these experiences.
So was I really free?

What's wrong with people doing whatever they want? Why would chaos ensue? Are all people just mindless brutes?

There has always been a social contract with the tribe. If you don't behave then you are out but at the same time the rules seem to be very very different for wealthy people.
About 15 years ago there was a posh London lawyer and his wife who got caught with around £5000 of crack cocaine.
It was a scandal because they were well connected.
All that they got was probation and a fine. They went home.
I got caught (many moons ago) with less than £20 worth of crack.
I was imprisoned for 2 1/2 years despite having a clean record at age 30 odd , which isn't usual for people caught with drugs obviously.
There is no free will in poverty or when one is not free from violence.
Being given free will by a supernatural being is a moot point when one is trapped by one's actual material situation.

Heck yes! The stupidity of people putting thing out their a** and poisoning the mind of innocent children with this garbage and a fear of nothing does anger me.