The "act like a man", or act like a woman" thing is a common misunderstanding. A lot (not all) of traits that men and women have that are assumed to have a biologically nature, are in fact environmental. It's whatever the norms of the era dictate. In America, It was normal for women to have mens looking haircuts in the early twentieth century. And, I can't remember when this particular period was, but there was a time that little boys wore, what would today look like girls clothes.
We're (mostly indirectly) taught at an incredibly young age what is and isn't acceptable for boy and girls to do and like. Young girls are discouraged from being funny at a young age while boys are encouraged. That's why there have always been far more male comedians. The "women can't be funny" belief also stems from that. Science as well. It's not that women aren't inherently uninterested in the subject, they're just discouraged from pursuing it.
And men too, are also negatively affected gender norms. Boys are taught and expected to be tough and have a strong backbone. crying and a weak personality is expected of woman. you know the "be a man" term, of course. Also, ever wonder why for a long time men didn't cook, but for some reason they grilled? Well, that's how grills were marketed. It was an established men's activity due to that, and was taught as such.