One of the most unsettling suggestions that sociobiology makes about mate selection is that women, in effect, select men who will create patriarchy.
Women try to create and maintain equality in their social network. Deborah Tannen shows the dozens of ways in which women's talk is designed to end up with both speakers on the same level. One of the most common gambits of women's conversation is for the first woman to deprecate herself, and the second to deprecate herself to an equal degree, establishing a bond through their shared troubles.
Men, on the other hand, have dozens of ways to establish who is one-up or one-down, to use Tannen's phrase. Men's organizations are hierarchical. Men's play is designed to produce the most competitive game and end up with clear winners – even if the players don't know one another's names.
In their relations with one another there are ample ways in which men's and women's social styles can cross one another up.
Men who are well-adapted to competing within a hierarchy, and have good prospects of rising within it, have a real skill that will help them succeed in life. They are likely to accumulate just the resources that would be most helpful in supporting a family. Women are more likely to pick men who will be good resource providers. SO, women are likely to choose men adapted to hierarchies.
It is a step, though, from saying that women tend to choose men who succeed in hierarchies, to saying that women choose patriarchy. When men and women talk using their normal styles, men are more likely to end up in the one-up relation with women. This does not come, I think, from men's innate desire to dominate women, but from the clash of their normal communication styles. If she takes a one-down position, expecting him to come down equally, and he takes the one-up position she has offered, because that is normal to his way of interacting, she is left, inadvertently, one-down. And more often than not, if she got there by telling him of her troubles, looking for sympathy, he is a likely to try to solve her problem, to her great frustration.
Willy-nilly, then, men and women may find themselves in hierarchical relations. And men who succeed in hierarchies are more likely to get selected as mates. The next step, though, to patriarchy, I don't see as necessary, even if is a frequent outcome. The hierarchy of men over women is not valuable to men or women for its own sake. I can't see how it makes evolutionary or design sense. There might be some situations when the family/clan/band is living on the edge of survival and therefore the group needs strong and clear hierarchical order. In those situations, I would expect most bands to be led by men. But in the normal family in modern society, I can't see the need or the advantage of a default gendered hierarchy. The normal pattern, as I argued in the discussion of male headship, is that he comes home from competing in a hierarchical world, and usually she does, too, to a household in which she makes almost all of the daily decisions for the family.
SO, I can see how women select for hierarchy in society. I do not think women select for patriarchy in society or at home.