Why were the men at the synagogue in Nazareth so upset with Jesus in Luke 4:23-30?
The reason why the men in the synagogue are angry at Jesus can be found before the verses that you actually cite. Most of the reason why they are angry at him comes from Luke 4: 16 to 22. In those verses, we are told that Jesus gets up in the synagogue and makes a certain claim.
In those verses, Jesus stands up and reads from the book of Isaiah. There, he claims that he has been anointed by God. He essentially says that God has chosen him to be a major prophet or even the Messiah. This seems very presumptuous to the men of Nazareth. As they say, this is a man that (as far as they know) is just the son of Joseph the carpenter. They wonder why he thinks that he is the anointed of God. Jesus basically tells them that prophets are never given proper respect in their own homes.
This means that Jesus is claiming to be a very important religious figure and is essentially rebuking them for not realizing that his claim is true. This makes them angry as they feel he is being blasphemous. Therefore, they chase him out of town and seem to want to kill him.