It would pay to bear in mind what SORT of education occurre in roman schools:
For the most part it was rote memorisation of the letters and the sounds they made to give literacy and very little else. A roman education was not a 'Greek education', rhetoric and logic were not taught.
Mike Duncan's 'a history of Rome' podcast was very informative on this and though Marcus Aurelius would have had private tutors for these things that is really what he was likely talking about when he says to have in the home
Did you mean Roman public education only taught basic literacy? For aristocrats, pupils were taught Greek and Greek literature early on since later republic era. Julia Caesar's mother went so far as to have a Greek slave accompanying Caesar from early childhood so he grew up bilingual. Marcus Aurelius was as comfortable in Greek as he was in Latin. His extensive training rhetorics is obvious from his writing. He wrote "Meditations" in Greek, because that was the language of philosophy.
Mike Duncan's 'a history of Rome' podcast was very informative on this and though Marcus Aurelius would have had private tutors for these things that is really what he was likely talking about when he says to have in the home