You did not misunderstand me. I made myself clear.
If government schools were to suddenly be dissolved, what solution do you have for teaching kids?
In the first place, you inserted the word "suddenly", not I. In the second place you are assuming that someone is teaching (anything worthwhile)to these kids now. Bad assumption in many schools.
The freemarket and homeschooling can educate the kids in fairly short order once they are allowed to do so. I think you would be amazed at how quickly things would change in the absence of government force.
Back in the 1800's the government encouraged the churches to educate our children. They provided incentives and grants to them.
Real schools.