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It seems to me the point you are making is that you take issue with the choice of wording (“unskilled”) and I do too. That doesn’t mean it doesn’t represent a real category. It’s school vs no school so use that word if you want. If tomorrow I want to apprentice as a plumber I can, if tomorrow you want to be a researcher in artificial intelligence you can’t. You can pick the wording but that’s a real distinction: a job board in your town will hire a line cook with no experience, or an apprentice tradesman with no experience, but that is not true for every single profession. They all take skill in the long run, some have a barrier to entry and THAT is what the words (which are badly chosen admittedly) are for.
“No school” still requires raising someone, negating it because it’s shared doesn’t mean the labor didn’t require a large input beforehand to be done.