This is an extreme statement which bundles together a lot without direct evidence.
Written in an era in which there was a lot of pro-Democracy and anti-Communist discussion, Hutchins is making an almost religious statement here which binds education and democracy in the ways in which the Catholic church bound education and religion in scholasticism. While scholasticism may have had benefits, it also caused a variety of ills which took centuries to unwind into the Enlightenment.
Why can't we separate education from democracy? Can't education of this sort live in other polities? Hasn't it? Does critical education necessarily lead to democracy?
What does the explorable solution space of admixtures of critical reasoning and education look like with respect to various forms of government? Could a well-educated population thrive under collectivism or socialism?
The definition of "natural slavery" here is contingent and requires lots of context, particularly of the ways in which Aristotle used it versus our current understanding of chattel slavery.