We want to socialize our children and not leave it up to other children their age who care nothing about our culture, our beliefs, our norms, our values. Of course, socialization lay at the heart of the classical gymnasium, but it was all about transmitting a culture from one generation to the next, not about crowding young people of identical ages into rooms where they were instructed and drilled in basic skills. There is an interesting historical parallel to our dilemma. It is Rome, the Republic that became an Empire after which our own Republic close to being an Empire was modeled. Rome, too, had little if any culture of its own, or perhaps it is fairer to say that its culture, like ours, was derivative, first from the Tuscans, later from the Greeks, and later still with influences from Africa and Asia.
Greek culture is what the Roman schools of grammar, rhetoric and philosophy taught.
Indeed, virtually all the teachers were Greeks who began their teaching careers as slaves tutoring for a family. Those who were manumitted for rendering good service in this role typically established fee-charging schools of grammar or rhetoric as freedmen. Well, to begin with, grammar had little to do with the study of rules for decoding and manipulating a symbolic language like Greek or Latin. It entailed the reading of literature and above all the careful study and extensive memorization of Homer. Homer was not just a ripping good story.