What about wanting to quit their jobs and take care of babies? That’s social/behavioral, so part of what you’d call gender. But it’s also rooted in biology.
It's not just cis women who want to do that though. And there are many cis women and trans men who don't. Not to mention, part of why it might be the case that women tend to quit their jobs and raise kids is because there's a lot of societal pressure to do that, and until relatively recently women (in the US at least) haven't really had the right to be independent at all.
Women not only do, but express the preference to, stay home with kids at much higher rates than men. It's quite likely there is a biological reason for that, and that the social construct derives from that instead of the other way around.
The fact that some women don't want to stay home and some men do doesn't mean it's a social construct. Many biologically-rooted differences between men and women are expressed in the population as overlapping but not coextensive normal distributions. E.g. https://link.springer.com/article/10.1007/s00421-006-0351-1