I don't think the two quotations are incompatible. Aurelius seems to be advising that no penny should be spared on providing a good education (and thus prefers hiring a tutor for 1-on-1 tuition). The Chinese quotation advises against children being educated by their direct families. Presumably public education was better in China at the time (see my sibling poster about Roman schooling), so public schooling was the "best" alternative, whereas in Aurelius's time hiring private tutors was.

My main concern with home-schooling is that it sort of sets an upper bound to the child's learning of that which the parent knows. (although I'd guess it works quite well at younger ages provided the social contact with peers is still maintained in some way).