Gender is all about social interactions. For example, blue and pink being "masculine" and "feminine." Is there any relation to male or female chromosomes that would make blue appropriate for someone with X and Y chromosomes, and pink appropriate for someone with 2 X chromosomes? Of course not. Same goes for wearing makeup or high heels. At a different time in history, those things would have been considered "manly" but over time that's changed. None of the social flags that we use to determine a person's gender have anything to do with their genitalia or chromosomes, because we generally don't have that information when we see people in public. If gender and sex were really the same, it might be a bit more difficult for pre-op trans people to pass for a gender other than the one they were assigned at birth.

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

The science is a actually not settled on the reasons for the blue/pink preference.

Same for a lot of what trans activists want to pass as facts.

Tolerance and fighting discrimination is important but bullying people into a set of beliefs is doomed to fail, except on Twitter until today ;)