The thing is that it's not particularly one or the other (nature or nurture.)
Personality and behaviour is a a complex mix of nature, nurture and accident.
Humans are extremely social creatures. I've just been reading this random vox pop article that I found linked to articles on genetics about social contagion: https://www.theguardian.com/science/2021/jan/24/the-five-emotional-contagion?CMP=
The research linked within it seems to be very much centred on being used to help reduce inner city violence and violence in Schools, mostly male dominated
Copying is one way we learn: The language of the group, after all, is “contagious” to developing babies. The behaviors that are most contagious are those that are the most emotionally engaging as well as the ones carried out by the people who are most relevant to you. Salience is key when it comes to the copying response.
The second mechanism of emotional contagion is the brain’s dopaminee* system, which works in anticipation of a reward. “Activation of that system puts you down a pathway toward what is important socially and for survival,” he says. If you anticipate that you will be rewarded for responding to someone with anger or violence, you are more likely to get on that behavioral track.
If you veer off or are shut out from getting a reward, Slutkin says, the brain’s pain centers are activated. “A sense of I can’t stand it lights up in the context of disapproval.” That’s the third part of this intricate biological system that keeps you on a path of emulating peers. In the case of the inner-city violence (and even school and other mass shootingss*) that Slutkin works to reduce, the path might be paved by a group that is thought to expect you to shoot someone who insults or betrays you and rewards you for doing so. If you don’t, you’ll be excluded.
We only need to spend a short time looking at toys and clothing for children to see how the "rewards" for behaviour is aggressively marketed to children from a young age, even if not within the family home.
My youngest likes the odd Lego magazine. Ninjago is all action and heroism. There are female characters but most are male.
A Lego friends magazine he got recently (Lego friends is marketed 'for girls') had an awful lot about tidying up your bedroom and being very kind. Which riled me somewhat - there's never any of that in ninjago! There are some male characters in Lego Friends but it's all very stereotypically female.
Lego city is more neutral thankfully, but he's never as keen on that.
Both my boys had cottoned on to basic gendered stereotypes from around the age of 2. By 3 we were having arguments about what colours boys and girls could like, despite all my attempts to be neutral.
let toys be toys and clothes be clothes have done lots of research on commercial gender stereotyping (both originated from mumsnet)