Your argument would be valid if there is no risk of very bad social or academic outcomes at a private or public school. But there are kids in the public school

Your argument would be valid if there is no risk of very bad social or academic outcomes at a private or public school. But there are kids in the public school system who graduate without being able to read and write and it doesn't take much to find students with extreme social issues. Perhaps the risks are just inherent in growing up?