After reading from the scroll of Isaiah 61, Jesus declares that the words of the prophecy are fulfilled at that time. He is claiming that the end of the exile as arrived and that the kingdom of God has finally arrived. This is a bold claim which appears to have been understood as a bold claim by the original listeners. Their reaction is remarkable for several reasons.
First, the initial response to Jesus is amazement (v, 22). The people are amazed because his words were “full of grace.” But what do they mean by calling Jesus the “son of Joseph” (v. 22b)? It is possible that the people are question the legitimacy of Jesus (John 8:41), but more likely they using the question to deflect the implication of Jesus’ words. By claiming that he fulfills the prophecy is to claim to be the Messiah, or something very much like it.
Second, Jesus is a bit harsh in vv. 23–24. Does he jump to the conclusion that they are rejecting him? Does he know what the people are thinking (as he does in Luke 5:22; 6:8; 7:40)? The meaning of the proverb is that Jesus is not the right person to offer himself as a fulfillment of the prophecy – who are you to be the Savior? This is not unlike the mockery endured on the cross, “he saved others, let me save himself.”
Third, the nature of the demand that the Nazareth congregation has in mind in v 23. If Jesus is responding to their unexpressed demands, what is it that they are demanding? Likely the people are requesting a sign to show that Jesus is the Messiah. Jesus never really does signs in response to a demand, therefore his response understandable.
Fourth, is the purpose of verse 24 to be a response to or justification of verse 23? “No prophet is accepted in his hometown” – this is the standard fate for a prophet! Jesus is not upset that his own town rejects him, this is the first of what will be many rejections in the gospel.
Fifth, does verses 25–27 imply a future Gentile mission? Some argue that the fact that Elijah and Elisha went outside of Israel and did miracles implies that Jesus will work outside of Israel and offer salvation to the Gentiles. But in the context of the rejection theme, it is better to see the analogy of Elijah and Elisha as rejected prophets who were not welcome in their own land, therefore the outsiders were the ones that were benefitted by their miracles. In Luke, as in each of the Gospels, it is the outsiders that are brought into the ministry of Jesus, not the good people of the synagogue in his hometown.
How ever we sort out these issues, the people are angry enough so that by v. 28 they are ready to toss Jesus over a cliff. This is not unlike the reaction to the speech of Stephen in Acts 7. Jesus simply walks away from them (possibly protected in supernaturally, cf. 4:10-11). From this point on, Jesus’ ministry focuses on “others” outside of his hometown of Nazareth.