As an American, I really appreciated this post!
In the United States, we have a variety of options as well - public schools (divided into general & charter schools), private schools, and you can also elect to homeschool your children.
The one that is the most puzzling to me, although I recognize that each child is different, is parents who choose to send their children to private school. As in China, there is a fee associated, but as local property taxes pay for your public school (general or charter) I struggle to find the justification for spending extra money on private school.
The other thing to note (sorry, this is longer than I intended when I started) is that there are a variety of resources in most communities that allow children the benefit of socialization while also benefiting from the personalized education they can get from home schooling.