There are tendencies that more men have than women, and vice versa, but there is no strict binary where we can truly say "all men are like this" or "all women want that" — even within the same culture — and certainly not for many other cultures. As already noted, these absolutes don't even exist in animals, so why would they be present in human animals who have more complex abilities?
We know from looking at other cultures and at different periods in history that maleness and femaleness are often expressed differently than in patriarchal cultures. The Mosuo of China, for example, are a matrilineal culture where mothers are the head of the family, and everybody lives with their mother or grandmother and her extended family. There is no such thing as marriage or even fatherhood, really, although men help to take care of their nieces, nephews, and grandchildren who live in the same house as they do. Men visit their lovers at night, and then go back to their mother's house. The women also do all the farming. Men care for animals and build houses.
Prior to the 4th c BCE, Egyptian women were the head of household, and conducted business (including legal business) in the marketplace while men stayed home and did the weaving.
In most Native American cultures, there were gender roles, but also a huge belief in balance, and sharing of power, as well as a lot of personal autonomy for women - something that white missionaries and settlers did their best to stamp out.
Most egalitarian cultures have gender roles, and then quite often don't pay all that much attention to them because personal autonomy is valued much more than performance of gender. Who cares what work you do, as long as you contribute to the group? In a few cultures, what work you do (and not your biological sex) is what determines your gender.
Imagined strict gender binaries are simply a way to justify the marginalization of women in patriarchies. I’m working on a story on the various mating and sex norms from other places in the world that show quite clearly that Evo Psych notions about that are just an invention of guys trying to make it seem like patriarchal paradigms are universal.
