There's a lot of things where it isn't advantageous to be a man, but there's a single one which is by far the hardest on women: reproduction. Men don't get pregnant, they don't have their bodies changed (sometimes permanently, as it happens to a lot of women - from stretch marks to fistulae, from the aesthetically unpleasing to the downright painful and/or lethal) and they don't feel any physical inconvenience caused by carrying a fetus inside them. A lot of women don't even have the luxury of feeling any pleasure when conceiving.
Men don't go through the pains of childbirth, they don't risk having their genitals torn and losing their capacity for sexual pleasure when their children are born, there won't be any doctor doing things they didn't consent to in a state of completely helplessness that might not only scar physically and mentally, but their child too. Men can't be victims of obstetric violence.
Men don't have the same level of attachment to their offspring - it's no wonder a lot more men leave for the proverbial pack of smokes to never come back than women. A man who abandons his child is just a deadbeat dad, a mother who does so is a monster. Men don't have their professional lives upended by having to raise children. Men can throw some money every month at their kids and see them only during the weekends and still be seen as a good dad and a desirable partner; women usually don't. If a man has a severely disabled child, there's no expectation he'll abandon his own life completely for decades to take care of the child.
If men don't want children, they can get a minimally-invasive surgery or wrap their penis with a thin layer of latex, which is nearly to no inconvenience compared to what a woman requires to not become pregnant: either complete celibacy, a highly invasive surgery - that might be denied to her even if she never had any desire to have kids for most of her life, sometimes she can't even make this choice without having her husband's formal permission - or taking hormones that might not even work (as there's a lot of trivial things that cancel the effect of contraceptive pills) and even give her something horrible like deep vein trombosis before her fifties.
All of that is terrifying for a lot of women, and I'd wager it's much scarier for women/girls who ARE educated. They know better what to expect in the worst case scenarios. It's no wonder they'd opt out of womanhood if they could.
