In rich countries (as the Economist again sets out), after parental income and education level are taken into account, state schools are mostly perfectly functional (while of course not perfect) and there is little evidence that private schools add much value.
Depends what you regard as evidence - many top U.K. universities take a much higher % of private school students than the proportion they represent (7%).
Which is why immigrants come here and scrimp to get their kids a good education to establish the family. Alternatively they may also help a family member pay international fees to go to a Western uni - to get a foothold in a Western country.
There are all kinds of factors not covered by state system here - anyone showing significant talent in music, sport, dance etc - may need specialist training that requires significant investment. There are no state specialist music schools here, example, like Chethams, Menuhin etc.
The famous Russian dancer Sergei Polunin’s whole family made huge sacrifices to get the best training for his talent. His father took construction work in Portugal because it was the only place he could find work, living apart from his wife and family, to fund his son’s place at the Royal Ballet School here. Ultimately the marriage didn’t survive.
You tell him his sacrifice wasn’t real, doesn’t count.
If you are middle-class, it generally makes more sense to invest in a property near a good state school (since our state schools actually education children quite well, unless the state schools in places like India) and then supplement with tutoring and so on
It makes sense for some middle classes to pay for education by stealth by buying places at state schools via property and tutors, depriving less privileged able students who can’t afford either, while other people choose to pay directly.
But this discussion was not about the merits of the private vs state system in the U.K. There are some excellent state schools here.
But of the principle that paying for education cannot be regarded as a sacrifice for some people.