I think this interpretation lets Coriolanus off the hook too much tbh. Yes, his mother and country have trained him for war and pride and domination, but they were also trying to train him to love Rome and follow Roman customs, and he signally failed to learn those lessons. He breaks custom by refusing to show his war scars to the plebeians during the consular election and then arguing that the plebeians shouldn't be allowed to vote anyway, and then storms off to ally with Rome's enemies to sack the city.

It's a classic case of someone who is fantastic at one culturally approved activity and believes that they should therefore be exempt from having to learn anything else. "I'm amazing at football, so why should I have to learn math or social skills?"