There is also a problem about "competition" that is also hitting the public schools. There is already some competition. Parents tend to locate where they believe they will get the best education. White Middle Class Soccer Moms look for the "best" school by doing internet research. They find one, then they move there en mass. What happens? The school has a large influx of people and the quality goes down. They need to raise taxes (the rates) to fund the new influx, and this ends up placing people out of the system except those who can afford it).

The solution is that they just reject or do not accept students (but they can't). A private school can. They cherry-pick to keep their relatively small, homogeneous populations of good students.