Why were the children of wealthy Romans educated in Greece?

Because they could afford it. The Roman education system was based on the Greek system, so why not learn it in Greece. The Romans education was based on the classical Greek tradition but infused with Roman politics, cosmology, and religious beliefs. The only children to receive a formal education were the children of the rich. The very rich families employed a private tutor to teach their children. Those that could not afford to do this used either slaves or sent their children to a private school.