Answer:
According to N.T. Wright, the people become angry and try to run Jesus out of town with the intention of throwing him off a cliff because of the additional words he speaks in verses 23-27. In these verses, Jesus refers to two specific instances from the Hebrew Scriptures, highlighting that God's favor and blessings are not limited to the people of Israel. He mentions the widow of Zarephath and Naaman the Syrian, both of whom were Gentiles and not part of the Israelite community.
This angers the people in the Synagogue because they believed that God's favor and blessings were exclusive to the chosen people of Israel. Jesus' inclusion of Gentiles challenges their understanding of God's plan and disrupts their nationalistic pride. They find it offensive and blasphemous that Jesus would suggest that God's grace extends beyond their borders.
Furthermore, by citing these examples, Jesus implies that the people in the Synagogue may not fully receive God's favor if they refuse to accept his message. This further aggravates them, as it challenges their sense of entitlement to God's blessings solely based on their ethnic and religious identity.
Thus, the combination of Jesus' widening of God's favor to include Gentiles and his implied critique of their exclusivist attitudes infuriates the people, causing them to react violently, intending to throw Jesus off a cliff.