The benefit for men in controlling women is controlling access to women for sex, controlling whose baby pops out of the woman's vagina, the partners/husband's etc, and making sure that the man has good standing in his community.
He may have one wife or twenty, but she had better not be sleeping with anyone else. If she does he might be emotionally hurt, he might be undermined, he may end up raising and paying for a child who is not his, his whole inheritance may be given away to someone who is not his kin.
This is all about what we have (female reproductive organs) it's not about what we don't have.
Before people settled down and started farming, I think (and I have heard this elsewhere so it is not just me), that people hunted animals and people picked berries, and people dug up roots.
What would be the point of the men chasing an animal for 50 miles only to kill it and say "Kids, wife, dinner is ready, oh hang on they are back at the rock fifty miles away."
I am not so sure that early humans had such well defined roles as one person (with a vagina) picks berries and one person (with a penis) kills an animal. I am sure that came in, with time, but early people I think not.
So our oppression, for another's benefit is absolutely about what we have got. What we have got which is worth controlling. The people that colonized other lands did not go there because of what the other people did not have.
However, men do appear to have taken it all a step further, innovative lot , and seek to oppress, or police, how other men act, and then yes, they do appear to oppress other men who do not fit their own high standard macho-ness of what being a man is about.
Poor people, people of colour, people of different religions etc all do get oppressed by others. Yet even in these oppressed groups it does seem women and girls are also singled out for additional oppression from within their own group by their own people's.
Sometimes this oppression is done by women, FGM, foot-binding etc but yet it still serves a purpose for men. FGM survivors will be unlikely to seek sex outside the home, women with bound feet cannot run away.
I really cannot see how any of this is about what we do not have, it is what we have which is valuable and because we do not have a sticker on our head saying 'fertile'/'infertile' then I think women are all lumped in together.
Nowadays some men would run a mile rather than have kids but the pattern of oppression for some is so established it does seem far removed from our fertility. Yet 'domestic' violence and abuse and control often begins when a women gets pregnant.
If these do not seem quite good reasons for young women to want to identify out of being female, especially if they are lesbian or are not keen to get married or have kids or whatever, I am not sure what is.
However, we need the young to fight this and change things for the better for all people.
Phew sorry that is long, I must go and do some stuff. Fortunately not the washing up - hubby is doing that. Remember it's not all men who are mean and nasty!