As you've pointed out, in a patriarchy, preserving the rights and privileges of men is primary, even above and beyond the value of children - which they are ostensibly concerned about, but only as patriarchs.

"It’s not that men and their mothers in these societies don’t care about children. They do, often desiring lots of them, especially several sons (an heir plus a spare). But preservation of the patriline and patrilineal institutions still takes priority.

Hrdy, Sarah Blaffer. Mothers and Others (p. 265). Harvard University Press. Kindle Edition.

Thanks for spelling this out so well. It is indeed appalling that gun deaths are the leading cause of death for children in the US.