people are like "men get to lead and make more decisions, it's so unfair and sexist that wives are expected to be more compliant".
hello? we live in a society where well over 90% of people don't want to lead. most people hate the responsibility of making decisions. most people would rather someone else decided things so they don't have to think about it – and don't have to take the blame if it doesn't work out.
why would you want to be the "head of the household" when you find it hard and scary to lead? people struggle to deal with decisions. people doubt and hesitate, and struggle to lead since they aren't really sure where to lead to.
since wives get the role that most people prefer – that most people find more desirable – this aspect of marriage is sexist against men. right? wives are getting the better deal since they are less expected to deal with hard stuff that most people don't want and actively avoid.
our society pressures men to be more confident, have more leadership traits, figure out answers to more decisions, solve more problems, etc. it's putting more demands on men, more expectations, more stress, more worry, more hardship. women are given places in society where they have it easier. a few women want to be leaders and be in charge of lots of stuff – and they can do that (no one stops them in business, and they easily find a man who will let them wear the "pants" in the marriage). and the vast majority of women, who don't want that, don't do it. but what about men? they are under such pressure to be leaders (and providers and breadwinners), like it or not. if they don't do it, they are punished. there aren't plenty of women for them to choose from who will be happy with a weak man.
being more of a leader sounds appealing to most people, it sounds like a good thing, so they think men are getting a good deal. but if you look at people's actions – men and women – the vast majority prefer not to act much like leaders. people find being a leader hard/stressful/etc, and they run into problems like "i don't know what to do. how should i know what to do?" and they prefer easier routes.
would it be better if there were more leader-type people? sure. but sexism isn't the issue there. men have trouble leading, too. many men do some leading because they don't see any way to get out of it, but they are bad at it and have a bad time. it's not like men got a special upbringing that prepared them to be good leaders and enjoy it. they, too, had a childhood full of compliance to authority, being punished for taking initiative or exploring/experimenting, being punished for taking risks that don't work out instead of being really conservative, being punished for going first and pioneering anything instead of waiting to see what the majority do, etc, etc.
there are sexist aspects of parenting, which are nasty. overall i think they're worse for women. boys are pressured to suppress emotions, especially crying. girls are pressured to be pretty. there are many, many shared mistreatments and some gender specific ones.
regardless, it's so dishonest to be like "omg sexism, men get to lead more" without the speaker considering that they hate leading, and all their friends hate leading, and their father hates leading (usually, though not 100% of the time. and even if they won't admit it).
PS This is similar to the complaints about the lack of women in high paying jobs, and Jordan Peterson's reply that the main issue there is most people don't actually want or like those jobs, and women who have those jobs often quit because they don't want the stress, long work hours, etc. The women aren't quitting because of oppression, they're just making a reasonable decision to have some family life (or pursue whatever else they want) instead of just work hard all the time.