I was not debating the efficiency of the private schools visavi public schools. Introducing strawmen is stupid.
Also: home schooling has been illegal in Sweden since 2010.
More to the point, while it's mandated that people buy car insurance few people argue that that's not a 'free market' because regulation is not the same thing as a state monopoly. After-all people also need food.
Yeah, you got me (insert rolleyes).
Car insurance also doesn't operate on a free market, for the reason you cite. I don't care that "few people" would argue it (appeal to authority; you like fallacies don't you?). You seem to think that something is either a state monopoly or a free market, but it is not so.
PS: Most economists accept that many completely unregulated market tends to monopoly's which try to extract rents. However, once a monopoly shows up they no longer accept that it's a 'free market' so the term 'free market' does not mean what happens when government does not interfere with a market. After that it get's complected as to where the line is drawn between free market and something else, however the bar is surprisingly high as for example moderate sin taxes don't prevent free markets.