That's very interesting information.
2 children per woman seem reasonable in order to have a population with only a slight decline in theory. In practice if a system is gamed with a one child policy, it will be gamed with a 2 children policy, leading to effectively 3 instead 2 children.
Why do the poorer population parts breed and the richer ones are not capable of sustaining their numbers?
Wealth is not a goal if humanity does not survive. A human population that is not capable of sustaining their numbers is ill one way or another (the industrialized West qualifies as ill). A population that breeds into a Malthusian catastrophy is also ill, because they lack the ability to enact growth control based on conclusions about the future.
Population development control is a mechanism of a healthy society with sustainment and growth adapted to the commonly available means. A problem is the longterm static state of technological development that enables to foster this mindset in a society that feels to have a good predictability of their future.
Chinese one child policy seems to be rather enforced and does contain some leeway for a flexible two child reality. The outcome is a higher investment capability per child for success and a corresponding higher earning capability.
Many human societies have developed a good breeding concept, the deviations are usually signs of upcoming deep changes and corresponding insecurity about investment choices among males and females. The current wealthy class is most affected by perceived insecurity. Often they are clinging unto the wealth that is seen as highly threatened by having a rather normal divorce with offspring due to current interpretations of laws. For well-educated women the choice is furthermore between their dreams of being someone respected instead of a simple housewife. The housewife role is seen as a pastime of leisure, requiring no real qualification, and leaving them at the whimps of a man they turn into their patriarch by losing their economic independence and much of their negotiation capability within the relationship. The seemingly only solution worldwide for a society is to limit offspring to the poorer class that has less qualms about adverse effects on their wealth.