While it may appear to be nitpicking, I'd like to focus on the wording you used here to make an important point.
"Do we accept"
What is this "we"? You may hold one opinion while I hold another. More to the point, if I desire private unobtrusive education, it makes no difference if you approve of my decision, because the education of my child is solely my prerogative.
The collectivist bent you put on the issue: "our children", "do we accept" accepts as a matter of course that children are collectively owned, and that the parents wishes of their children's education can be forcibly overridden by the collective.
This begs the question: Are we free people with self determination, or are we farm animals whose decisions are made by a farmer that calls himself government?
Anarchy coool!!!!
It isn't nitpicking at all. This is the crux of the problem with folks that think like this. They think that society is some kind of organism. "We" is meant to imbue a group of individuals as some kind of undivided and contiguous whole, where the whole is somehow lesser than it's parts. When in fact the whole is greater than its parts. There is a fundamental flaw in this philosophical thinking that ignores the individual. Leaving the individual out of a philosophy is like building on sand. It is an axiomatic mistake.