I think he’s on to something. That wasn’t the best way for him to phrase it, though - yes, kids in school already are unemployed, but they’re supported by their parents because they’re considered to be on the path to getting a job. If they weren’t expected to be in school, I think he’s right that they’d be competing with adults for jobs instead of consuming with their parents’ money.
OTOH, would it be the economic catastrophe he suggests? I don’t think so. The parents would still have that money; they’d just do something else with it instead of buying things for their kids.
Considering how little of the secondary school curriculum is actually relevant to jobs, I think it could easily be replaced for that purpose by apprenticeships or brief trade school.
There doesn’t need to be a secret cabal. There’s an entire system of expectations and prejudices keeping things the way they are.