If your kid has your attitude, be prepared for the public school, the place where private schools send their problems. This is called competition?
Public schools are a conflict of interest. That they perform poorly is only one aspect or the problem. Public schools are by nature there to serve the interest of the government, not the student. Children are prepared in public schools to obey authority, to not question rulers, to recite mantras, and mostly how to be institutionalized so that should they graduate to prison, they will know how to act.
What public schools do NOT prepare children for is critical thought, investigative curiosity, questioning dogma, developing a standard of ethics, valuing integrity above authority.
Yes, it's true that public schools fail to teach math, science, music, legitimate history, etc. But that is a symptom of the issue. The actual issue is that public schools are intended to indoctrinate a subservient populace, not educate a free people.