What does Matthew 13:58 mean?

Luke's description of a visit by Jesus to His hometown of Nazareth includes a demand from the people that Jesus do the kinds of miracles they had heard He had performed in Capernaum (Luke 4:23). This might be the same incident Matthew refers to here, or a subsequent visit. In either case, Jesus refuses. This verse shows that He would not do many miracles in Nazareth because of the unbelief of the people. This is consistent with His response to similar demands from the Pharisees (Matthew 12:38–39). Such people are not sincerely asking for proof—they're ignoring the evidence they've already seen, and insincerely demanding more.

Matthew notes that Jesus "did not" perform many miracles, for that reason. Mark indicates that Jesus "could" not, but not because Jesus needed people to believe in Him for His miracles to work. Rather, this is much like saying "I could not give my son a reward, because of his bad behavior." It means Jesus could not appropriately do something, since it would contradict His message, not that He was physically incapable of it.

Jesus was the Son of God and filled with all of God's power. He could do whatever miracles He wanted to. Yet as Jesus emphasized to those He healed, He responds to requests inspired by faith (Matthew 15:28; Mark 10:52), not disingenuous demands for proof (John 2:18–19; Mark 8:11–12). The fact that the people of His hometown refused to believe that His power came from God gave Him little reason to demonstrate His power to them (Matthew 7:6).