No doubt some parents taught their children such things as the 3 R's, if they could read. Some Indian children were taught by missionaries.
It was publicly-supported education that made America literate.
Unfortunately, they don't do that in public schools very much anymore.
America was a highly literate nation long before the advent of public education.
I would assume today that if we eliminated public education today that all parents who truly cared about their children would take responsibility for their education. Why should I have to take responsibility for any else's?
What about Abraham Lincoln?