While it is true that parabolic teaching existed among Jews, Greeks, and Romans; Jewish parables weren't really within the "Greek Rhetoric" category, imo. Take for example, Paul, who said, "I may not be a trained speaker [referring to a formally trained Greek rhetorician] but I do have knowledge" (2 Co 11:6a). At the same time, Paul did speak at rhetorical gathering places (e.g., Mars Hill) though he wasn't a trained Greek philosopher. Other Jews, however, were more educated in philosophy as with Philo of Alexandria. But in the NT we see no formally trained Greek philosophers.When Jesus preached so strikingly in parables, he did not create a new literary genre. Rather, he made brilliant use of a genre which was already of long tradition and which was familiar to all throughout the Mediterranean world. In Greece and Rome, parables were employed by rhetoricians, politicians and philosophers. Perhaps the most illustrious among those who made use of them were Socrates and Aristotle. An interesting question is to what extent the classical parables are like those of the Bible. (The reader may wish to peruse Aristotle's discussion of the parable in The "Art" of Rhetoric, Book II.) In Israel, parables were uttered by prophets and wise women and men. They appear even in the oldest books of the Old Testament. Parables were often used by Jewish rabbis who were contemporaries of Jesus.
One interesting point on this was the fact that, in the first century, "travelling philosophers" (rhetoricians) were becoming increasingly popular. Live speeches were replacing what was formerly taught in schools and/or read in books. So the "circuit" of Paul and other NT teachers (Apostles being sent two by two) was something fairly new for Jews from what I understand. The Jews had had missionaries but the poplarity of "live speakers" was on the rise. Related to this was that when people wrote epistles (letters) or Gospels, in the case for Christians, to a far away community; the author wrote with the knowledge that their writing would be read by an assigned "reader" at the point of destiny. When I read the NT I often wonder what it would have been like to hear a NT book "aloud" for the first time....wow!
What specifically differs the from Jews, Greeks and Romans is rabbinical teaching (link): their "Halakha". Every rabbi was expected to develop his own teachings. In the Gospels we see Jesus engaging in Halakhic-dialogue in the Temple with the Sadducees and Pharisees. The standard form of debate was question-answer with the answers often appearing in the form of another question. Or, a kind of anticipating the answer (thinking out loud?): "If I say to you, you will say..." (which can be seen in Romans and the Gospels). And we see Jesus often saying: "You have heard it said ___ but I say to you...". This was rare. Quite rare, as Halakic-debate was essentially dialectical. Jesus was claiming to know THE truth. In other words, His Halakha settled the matter once and for all. "Who is this fellow that speaks with such authority?" the Jews asked. Rabbi so & so said, but Rabbi such & such said, to which Rabbi what's his name said, but Jesus said!
In reading the Mishna and/or Talmud; they read "like" the NT at times.
Rick