I know it's not usual for our culture but it is highly typical human behavior and is in fact one of the primary survival strategies that our ancient ancestors used to survive. Nomadic forager tribes still use it today. There aren't a lot of rules because there is a huge amount of personal autonomy, but anyone who gets notions about power, or a big head is going to be brought down a peg by the group - gently at first with teasing, and then progressively less gently with things like banishment from the group.
“When a young man kills much meat, he comes to think of himself as a chief or a big man – and thinks of the rest of us as his servants or inferiors. We can’t accept this ... so we always speak of his meat as worthless. This way, we cool his heart and make him gentle.”
Women spend more time with children than fathers in a patriarchy. It's not a "human" thing, it's a cultural/societal thing. There are current societies where men spend nearly as much time, even with very young children.
Fifty years ago women were second-class citizens by law in the US. There were literally hundreds of laws that applied to them that did not apply to men and they couldn't get home loans or credit cards in their own name to name just a few things. There's still a huge amount of structural inequality and unconscious bias in play - and every time women do make some inroads toward changing the culture, the backlash is swift and vicious. 73% of women journalists have experienced online harassment and hate, women surgeons get groped and harassed while assisting in medical procedures. The manosphere is a direct negative response to women changing the culture. I could go on and on, but you really ought to do your own homework instead of making me do it for you.
If you and even 30% of the men around you started exerting a positive influence on the men in your social circle, the culture would start to shift. We have the culture that we allow and the norms that we support. We all have to do our part, but since traditional norms of masculinity drive much of the violence and dysfunction in this culture, men have an outsized role to play in challenging them.