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No. We should finally end this myth. It serves nothing but fuel the primitivist bullshit and its derivations from anarcho-whatever and chuds retvrn-to-tradition. We should value progress, just the controlled one instead of capitalist anarchy of production.
Similar in Poland. At elementary and middle education level private is massively expensive but also usually better though that is mostly because constant cuts to public education means that regardless of failing birthrates there is always too much kids in class and too much duties for teachers. At those levels there are no pressure about it though, nobody is even asking which school you finished. But at university level state universities are free and much better while having much more competition while private schools are usually much worse.