“And Jesus said to them, "A prophet is not without honor, except in his hometown and among his relatives and in his own household." And he could do no mighty work there, except that he laid his hands on a few sick people and healed them. And he marveled because of their unbelief. And he went about among the villages teaching.”
Mark 6:4-6 ESV
Curious as to everyone's views, as to why He could do no mighty works there. Obedience to the Father is what I assume from a quick reading.
Jesus could/would do nothing without the guidance of the Father (see John 5:19-21, 30, for instance).
So what was the purpose of the miraculous works of Jesus and His disciples? To demonstrate that the Kingdom of God had come upon those who witnessed/received the blessing.
These works of God were designed to be a witness, but some people (many people in some instances) were closed off to God and a miraculous work would simply harden them to what God was doing.
For Jesus to perform miracles in front of those who would reject Him would simply harden them to the gospel. It is a loving act NOT to 'cast pearls before swine.' Perhaps when they are willing to receive a sign, they will receive one. Jesus has given even those who are hostile to Him the sign of His death and resurrection (Matthew 16:4).
When I witness to others and the person turns hostile toward me, I will generally shut down the conversation in an attempt to keep that person from hardening themselves to truth. It is an act of love and compassion. I will often explain that they get to "win" the argument because I am not going to put them in a position they will regret at the final judgment. Sometimes that reopens the conversation, with them realizing that my ego is not tied up in what I am saying. Other times that's simply where it ends. I don't shut the door for them forever, but I also don't approach them again unless they are willing to have a serious talk.