How about adding...

while government schools teach that truth is derived from authority

This includes subjects that you would never think of, such as English and Science

All bow down the greatness of Einstein who made a theory that is so complex that few will ever challenge it. However, the theory fails at every practical application. It is completely disproven.

But, as you said, school is not about teaching, about learning for yourself, it is about schooling.

And the reason "they" are afraid of homeschooling is that the children do not all get indoctrinated the same. The children will swim on their own, in their own direction, not as one with the school.