Illich wasn't against school per-se. He was against compulsory school, centralized pedagogy, and other attributes of a "modern" (ala 1970s) schooling system in Western social democracies.
He was particularly concerned with how the tenants of modernism affected developing nations (where he lived for much of his life) by pushing traditional methods into forced obsolescence in favor of ever-increasing reliance on social institutions.
His views on policy may or may not be on point (he seems most comfortable in the area of principle and theory), but the conceptual core that relates his views on education to his views on cars and medicine merits consideration.
He similarly wasn't against scientific medicine, but he thought the medical bureaucracy had outgrown its utility: that advances in specialized medicine were too expensive and served to prop up artificially unhealthy lives.
A strong line of his argument is that past a tipping point of size/power, institutions will create the needs they serve. We create these artificial environments where it's hard for most people to thrive and then we create social institutions to compensate: a social prosthetic.
The result in Illich's view is increasing passivity and helplessness: a petulant society composed of a disempowered citizenry.
The argument no-doubt merits a balancing counter-argument, but I find it compelling and it goes deeper than a simplistic dismissal of school.
> Even Nobel Prize winner Daniel Kahneman affirmed this consensus: “The hot hand is a massive and widespread cognitive illusion.”
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> Nevertheless, recent work has uncovered critical flaws in the research which underlies this consensus. In fact, these flaws are sufficient to not only invalidate the most compelling evidence against the hot hand, but even to vindicate the belief in streakiness.
The difficulty involves subtle misunderstanding of the probabilities involved in random sequences: an error that is nearly "nearly equivalent to the famous Monty Hall problem".