Girlwiththe I am one of these nonexistent women who worked full-time and whose DH was the primary care giver, doing the bulk of the wife work. He was a feminist and thought I was a genius. I would never have started my own business without his endless encouragement. When I started earning enough to support us he ditched his boring job and took over the DC full-time. I'm sure I chose a lovely, feminist man because my DF is one too.
We still live under patriarchy, though the condition of women in the UK is far better than women in, say, Pakistan. The pay gap is real, and women's rational wariness of men is the fruit of rape culture and social norms. Feminist men make themselves aware of this and actively combat misogynistic attitudes when they encounter them as well as making sure that nothing they do unintentionally causes women to fear them. Simple things like swapping pavements so a woman walking ahead will know she's not being followed
Men are responsible for 90% of serious and violent crime. Men are responsible for 98% of sex crime. This, of itself, has a huge impact on women's lives. I've been raped twice, and I know my experience is not remotely uncommon. Things like travelling alone, even walking in the countryside alone present anxieties for women that are not a concern for men.
If women's movements and behaviour in the public sphere are constrained, who benefits? The answer is the patriarchy, all those men who feel women have a place they should be kept in.
As the saying goes "Men are afraid that women will laugh at them. Women are afraid that men will kill them."
How we raise our DC can affect crime figures. Choosing feminist men to father our children will make a massive difference. Analysis of the many small and large systemic inequalities will help. It's being achieved bit by bit.