Except, of course, he doesn't really mean all: he just means Freemen.
Slaves and vulgar mechanics are not his concern. But once we take into account the fact that this is not the 1944 Education Act, the questions raised do cut to the quick in a way that resonates today: should education be more concerned with intellectual or moral virtue, and should it focus on what is useful or what is good?
The Freemen of Athens were fortunate indeed in that education was not designed to help them earn a living - "paid employments" are vulgar for they "absorb and degrade the mind" (hey, tell me about it). Hence, much of Aristotle's curriculum is about how to use leisure well. Certain subjects, not least reading and writing, must be taught because they are useful, but music should be taught merely because it gives "intellectual enjoyment in leisure".
We may no longer debate whether the Phrygian mode is superior to the Dorian, or whether the flute is "too exciting" to be taught to young people, but we do face dilemmas about the useful and the good. What are the implications of choosing to limit education for certain groups of people to the merely vocational? If formal education really is becoming more "useful" and less liberal, then youth workers may find an unlikely ally in Aristotle in justifying a wider view of education that takes in not just how to earn a living, but how to be happy and lead a good life.