That makes no sense. Most of this country’s history, there were no public schools. What makes you think the private sector wouldn’t do a better job?
There were public schools going way back. But then they weren’t called “Public Schools” until FDR came along and made them such. The government decided they could do a lot better than those country schools and city school districts like in NYC. If you’re in doubt, check this: http://en.wikipedia.org/wiki/List_of_the_oldest_public_high_schools_in_the_United_States