Capitalism is good for the market, and promotes development in technology, among other things. But a completely capitalist system isn't good for the school system and healthcare.
In fact, in a completely capitalistic society there would be no official school or healthcare, only private institutions.
A socialistic society may have better school and healthcare, as long as it doesn't tip over to a dictatorship with five-year plans. Those never work out. But even if the school and healthcare works, the free market wouldn't.
The best option would be a society with elements from both capitalism and socialism. Let there be a official system to keep the basic functions running, and provide as high of a quality as possible. And let there be a free market where competition is promoted. Let this include basically everything except law enforcement. Even if public school and healthcare is offered, let people be able to choose alternatives.
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You don't want to advocate socialism because the entrepreneurs will then just leave eventually to a different country where there are lower tax rates.
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True. You just have to find the right balance.