Masculinity and femininity are built on the same human chassis and share a lot of parts, share a lot of performance features, but the vehicles that roll off the assembly line are unmistakably different. The dogmas about masculinity and femininity manage to be a disservice to both sexes. It seems to me that there are some essential biological differences between males and females which are the basis for differing emotional affect. While acknowledging differences, there is also considerable overlap, and beside overlap there is plasticity. But men and women are different. Viva la différence!
To whatever extent men and women bond differently, one type of bonding isn't better than the other. (You aren't saying that, but I've hear it said.)
"Male culture" may reinforce the suppression of emotionality in boys and men, but a good share of it starts in childhood, under the management of women -- mothers, caregivers, and teachers. It's not something that most women do or (probably would do) deliberately, but boys are taught early on to control (suppress, really) their emotions. A good deal has been written about how current standard classroom practice is ill suited to boys: lack of recess periods (outdoor activity time, preferably twice a day); expectations that boys will sit still for a long period of time, and so forth. Boys seem to suffer more from this than girls do, but it really isn't good for girls to be taught to sit still all day, either.
Many children, boys or girls, have few opportunities to "go outside, play, and explore the world" because "the world" is perceived to be too dangerous, or in some places IS too dangerous. I grew up in a very small town in Minnesota and pasture land, fields, and woodland were very close by. A lot of urban folk simply don't have access to that sort of environment.
Later on, as boys reach early adolescence, then I think the influence of male culture (for better or worse) becomes a stronger influence.
We are all subject to a lot of influences -- peers, partners, parents, relatives, unrelated adults, school, media (whatever form), the church (for some people), the military, and so forth. The messages are multi-directional--be like this, no, be like that; don't do this, don't do that... etc.
I'm gay and 71, so... I don't have a huge amount of contact anymore with younger men, these days. As a gay man, I've associated a lot with other gay men--all ages--who
generally tend to be more emotionally 'available' and emotionally expressive. But the gay male subculture is a small part of the population. There are a number of middle age straight men at some groups I belong to that are extremely emotionally constipated -- just don't know of a better word to use. Some of them are just totally boxed in, others express their emotionality through intellectuality -- better than nothing, but not really healthy either. A lot of straight guys can't express approval effectively, and rather than expressing anger readily, they just slowly carbonize inside.
It seems to me that competitiveness is an essentially male feature. Biological creatures that humans are, we are not discontinuous with our evolutionary roots. Most male creatures compete for something--like mates, food, territory (food and mates). Brains and culture have helped us avoid the grind of individually scrambling for food and mates, but the drive is still there. So it often gets expressed on the freeway. I have to admit that when I am out bicycling, I like to compete with other riders (not that I'm much competition any more. Used to be.) It just feels natural.
Men, it seems like, are more likely to bond over work, or an objective, a battle, a cattle drive, clearing snow, taking down a tree, etc... than just over each other. Women "do lunch". Men get together around car repair--figuratively, if not literally..
Working together is one way that a lot of men interact. They can work on a project, hunt together, do sports together, build together -- all those sorts of things. Work provides a mediator they--we--can employ to bond and share.