https://archive.is/20231109141208/https://www.economist.com/china/2023/11/09/china-wants-women-to-stay-home-and-bear-children
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It's hilarious that capitalist rags like the economist want their lib readers to fear Xi by making him out to be some authoritarian conservative.
Also funny: central government wants local governments to invest in good toilets, the gall! How dare they support improving public services! 
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https://archive.is/20231109140845/https://www.economist.com/china/2023/11/09/xi-jinping-wants-china-to-have-better-toilets
The patriarchal family model is, itself, a consequence of property-based legal institutions awarding husbands and eldest male heirs the lion's share (even to the point of exclusive enfranchisement) of household capital, cash, and credit. Yes, of course men are going to dominate in a system that prohibits women from owning property or having a bank account or borrowing money.
It isn't even that the patriarchal model is outdated. It is that the individualist consumer economy contradicts and erodes the patriarchal model. And consumerism remains as much a part of Chinese culture as it does anywhere.
I'm not even sure if Xi is that opposed to patriarchy. Certainly, he doesn't seem shy about stacking his cabinet and senior staff almost exclusively with middle-aged and elder men. But he is quite clearly opposed to the excesses and wastefulness of consumer capitalism. And, in a country as big and resource hungry as China, it isn't hard to see why.