Well, you musta flunked history. Public schools were pushed by Horace Mann, an ex-Calvanist turned Unitarian. However, Mann couldn't establish the public school system alone. He was aided in his quest for "uniformity" by a Protestant backlash against the Catholic immigration of the time. They were dead set against allowing Catholicism to flourish and therefore were eager to capture youths in a nonsectarianism that was a staple of evangelical Protestantism.
The public school system, hence, is not a product of athiests (too few of us to do anything like that, really.) It is the product of Protestantism.