The Chinese, like many others, have children to increase the wealth of the family, to take care of the parents when they are old. The preference for boys is due to traditions of dowry and preservation of the male line.
Europe has a lower birth rate because child-rearing is expensive and time-consuming, and people want more money and leisure time. People in China also want more money, which is why the Chinese government uses monetary incentives to reduce birth rate. it is not necessarily strictly forbidden to have multiple children, parents must pay a “tax” (unaffordable to most).
In China there were massive problems with abandoned girls, especially in the country, where boys were valued more for working the fields. There was also great anger at the resulting diminished work forces of the family farms. As a result, the policy is much more relaxed in the countryside, with more children often allowed.
This is especially true if the first child is a girl; to prevent abandonments, parents are allowed to try for another. Even then, if it is another girl, they may get more chances.
If the first child is a boy, they have to stop there.
So in a sense, for some, the one-child policy has become a one-boy policy, and I’ve been told by various Chinese that some places actually have “too many” females, because of this development.
In terms of arguments against it… despite population control being a necessity, it has been clumsily implemented. There is much documentation of the negative implications of this, as western-media loves a bit of China-bashing.
I wouldn’t trust a ‘democracy’ to have handled the problem any better.