Okay. I'm gonna try to keep this short and light, please stick with me.

Gender is a social construct, like love or the economy. It's something humans made up to help us contextualize our experience of the world. Most of what we'd consider "masculine" or "feminine" behaviour is socialized, rather than genetic or inherent to a set of genitalia. You can argue that sexual hormones lead to a tendency towards certain types of behaviour, but no amount of testosterone is going to make someone care about sports if they don't, or good at fixing cars, or physically abusive. Men tend to gravitate towards "manly" things because they are socialized to - if a little boy wants a Barbie, a lot of parents wouldn't let him have it. He doesn't get opportunities to explore femininity, so is pushed towards being masculine.

And you might already be well aware of this, but s*x and gender are two different ideas, with the basic distinction being that your s*x is a purely physical trait, it's about what your body is, whereas gender is a social trait. And there's a whole spectrum of what this can entail. Someone whose s*x is female but who dabbles in masculine-gendered activity might be called a tomboy. If they feel uncomfortable with female s*x, or even just very comfortable presenting with an entirely masculine gender, then that could lead to them identifying as transgender - a gender other than the one they were assumed to have at birth that aligns with their s*x. They might think of themselves as a man, and might seek to change their physical s*x to match.

Now here's where the butter meets the biscuit - while "s*x" and "gender" are now (in certain use cases at least) defined terms, words like "woman" and "man" are much looser. Society has always defaulted to assuming that s*x and gender will line up, so what is considered a man socially and what is considered a man physically have always been conflated. The thing is, though, unless you're running a single-s*x sporting event