‘And he said to them, “Doubtless you will say to me this proverb, ‘Physician, heal yourself', whatever we have heard done at Capernaum, do also here in your own country.” '
Thus Jesus chides them because of their attitude, and puts into their mouths the words that they wanted to say, ‘Physician, heal yourself.' In other words ‘get yourself sorted out'. These words probably mean that as He has not performed any miracles in Nazareth He needs to heal Himself so that He could perform in Nazareth what He had performed in Capernaum. They did not pause to consider that the reason why nothing had happened in Nazareth was because no one had brought their sick to Him (contrast the people of Capernaum in Luke 4:40). And this was because they found it difficult to believe that the local carpenter could be a healer.
Others have read ‘Physician, heal yourself' as meaning, ‘Physician heal your own townspeople as well.' That healing is certainly what they wanted, for they wanted Him to do in Nazareth what He had done in Capernaum. Indeed what follows suggests that there was a great deal of antagonism because He had not done so.
Some have suggested that it meant that He should remember that He came from a poor family and better Himself before He sought to lecture others. What could He know of helping the poor when He was poor Himself? But that would not connect with the next phrase.
‘Whatever we have heard done at Capernaum.' Note the note of doubt. They had heard it, but they were not convinced that it was true. (Nazareth was a little cut off from the mainstream of life).