I think men and women are just too different in their biological instincts, which have been compounded by many centuries of societal pressure and tradition.
These are generalisations but women are more likely to want children (and have further children), have no choice but to bear the children, want to take on the primary care role (often dropping to part time or taking less demanding roles that allow them to "be there" more), less willing and able to put children's needs out of mind (mental load of school admin/ play dates/ activities/ healthy eating/vaccinations/dentistry/new shoes/ screen time limits).
Conversely men seem to be: less interested in having children, less interested in being the primary carer/default parent, unwilling/uninterested in stepping back in career, give less thought to all the minutiae of raising happy healthy children. I'm not saying they don't care, but in general much less engaged with such thoughts and worries.
Men are hugely privileged even if they don't realise or actively deny it. Moreover most are pretty happy with the status quo of at least nominally traditional roles. Even if they deny it many tend to find housekeeping and child rearing dull, unrewarding and demeaning - but think it's ok for women to do that (because they are inferior???)
The happiest marriages I have observed seem to be ones where the husband has the big career, the woman has the main responsibility for house/child rearing, and they both appreciate each other's roles and efforts. However, the woman is definitely playing the second fiddle.
The traditional model is sadly also a trap for many women, particularly if they dont have appreciative and fair minded husbands.
I would say I am happily married and we have an equal/ fair set up whereby I certainly don't play second fiddle. But I've had to fight to maintain those boundaries. My husband was prone to making assumptions without a moment's thought. I.e. that I didn't need one of the weekend lie ins because I'd wanted a baby so much (he was less keen) I should surely want to spring out of bed to attend to my special hobby. Don't worry, I soon corrected him on that. But there are numerous things that have cropped up. I didn't change my name on marriage. He asked if I wasn't proud to be married - I retorted that if he thought we should make a name change an outward sign of our pride he could change his name to mine. What a surprise - he declined.
He will forget to look in school bags and complete forms for school trips and reply to party invitations. I've tried leaving him to it and the result is that the kids lose out. His response is typically "of course I would have done it but you didn't remind me". No one reminds me though! We've been together 25 years and despite my attempts to change this he just doesn't give it a thought. It's either that he's not programmed for it, or secretly believes (but denies) that it's women's work, or a combination.
We've managed an equilibrium that I can accept in that he has some set roles that we agreed are his responsibility and I will not assist unless he expressly asks. So he is in charge of: all laundry, all hoovering, children's uniforms (including replacing) and children's dentistry, as a few examples.
Some men though would not even contemplate/tolerate having their privilege challenged in that way. I suppose my secret weapon was that I would have preferred to stay single and childless than play the second fiddle. For many women that's not an option they'd be happy with.
I don't really know what the answer is.