Because one school will be better than the other. Most likely the private school, because they charge money for parents to send their kids there in addition to the money they (unfairly) get from the government. So families with more money are more likely to send a kid to private school, which immediately creates social stratification between the private school kids and the public school kids.

The private school kids will perceive this inequity, even subconsciously, and internalize that they are better than the public school kids on some level. Often the private schools are religious too which is another can of worms.

I could keep going but I think that's enough to get the point. Private schools shouldn't exist. All the money given to them should be given to public schools so they are better for every kid no matter how much money their parents make.