I am not against private schools. I am more fully in favour of the individual making their own choices than I am about anything else.
My parents (public school) had very strong ideas about the benefits of comprehensive eduation and (they told us) it was particularly important to the comprehensive experiment that people like us (comfortably off, seemingly intelligent) were not creamed off to private schools, leaving behind the less well off with the less motivated etc. So, according to them, it is the parents who scrimp to keep their kids out of state schools are responsible for failure in the State System.
Chris Woodhead (bless him) was involved in a group of no frills private schools called Cognitas.
If I lived in the place I used to live in London, I would privately eduate, home educate or move. That act would make local state education worse. It's a toss up between doing the best for the country, or for the future skills base of the country, and doing the best for one's children. Most people, I think, would put their children first. I would, if the local school featured stabbings.
Putting one's children first is a natural, admirable human action. But don't, DON'T make out in any way you are doing the state system a favour.