Why did Peter use the rebellious-son language when speaking to Israel?
Peter used the rebellious-son language to bring Deuteronomy’s picture to Israel, showing they had treated their Christ like a rebellious, drunkard, wicked son: they killed Him and hung Him on a tree. In reality, He became that on our behalf, becoming sin for us.
Les explains that Deuteronomy chapter 5 describes an incorrigible rebellious son in Israel: he was so wicked that his parents turned him over to the authorities, and the Jewish authorities would order him stoned. Then, to make him a public spectacle and teach the lesson, they would hang the dead corpse on a pole in an extreme situation. Peter brings that picture to the nation of Israel, showing that this is what they had really done with their Christ. They had considered Him like a rebellious, drunkard, wicked son, and they killed Him and hung Him on a tree. In actuality, however, He became that on our behalf; He who knew no sin became sin for us. Les also stresses that the crucifixion was awful and not beautiful. It was a curse, because God laid on Him the sins of the whole human race.