I suspect it’s more that China doesn’t really have an old-age care health system, it has the age-old familial system: parents are looked after by their eldest son in their old age, especially in more traditional areas.
Which is one reason why sons were so important: daughters when married off became part of their husband’s family, and she would be looking after her parents-in-law. If you’ve only got one child, and he’s a son, then you might be OK. Hope he stays around and doesn’t die. If you’ve got one child and she’s a daughter, then hope she’s got enough overhead to look after two sets of parents in their dotage at once.
As I understand it, the CCP likes to emphasise Confucianism for its threads of “look after your parents, look after your neighbors, obey authority and don’t make a fuss”. But with that comes the “and a child’s duty is to look after their parents”, which implies that with a shrinking and aging population, will remove more and more labor capacity from the economy as they’re taken up with caring duties with fewer people to share the work around.
Note well: This is my deeply oversimplified understanding of the culture of a huge, disparate, heterogenous place which I am not from. When presented with contrary information, ignore me.
