Healing of a man with a withered hand/Why does Jesus heal on the sabbath?

Mark 3:1 And he entered again into the synagogue; and there was a man there which had a withered hand. Matt 12:9 And when he was departed thence, he went into their synagogue: 10a And, behold, there was a man which had his hand withered. Luke 6:6 And it came to pass also on another sabbath, that he entered into the synagogue and taught: and there was a man whose right hand was withered.
Mark 3:2 And they watched him, whether he would heal him on the sabbath day; that they might accuse him. Matt 12:10b And they [the Pharisees] asked him, saying, Is it lawful to heal on the sabbath days? that they might accuse him. Luke 6:7 And the scribes and Pharisees watched him, whether he would heal on the sabbath day; that they might find an accusation against him.
Mark 3:3 And he saith unto the man which had the withered hand, Stand forth. 4 And he saith unto them, Is it lawful to do good on the sabbath days, or to do evil? to save life, or to kill? But they held their peace. Matt 12:11 And he said unto them, What man shall there be among you, that shall have one sheep, and if it fall into a pit on the sabbath day, will he not lay hold on it, and lift it out? 12 How much then is a man better than a sheep? Wherefore it is lawful to do well on the sabbath days. Luke 6:8 But he knew their thoughts, and said to the man which had the withered hand, Rise up, and stand forth in the midst. And he arose and stood forth. 9 Then said Jesus unto them, I will ask you one thing; Is it lawful on the sabbath days to do good, or to do evil? to save life, or to destroy it?
Mark 3:5 And when he had looked round about on them with anger, being grieved for the hardness of their hearts, he saith unto the man, Stretch forth thine hand. And he stretched it out: and his hand was restored whole as the other. Matt 12:13 Then saith he to the man, Stretch forth thine hand. And he stretched it forth; and it was restored whole, like as the other. Luke 6:10 And looking round about upon them all, he said unto the man, Stretch forth thy hand. And he did so: and his hand was restored whole as the other.
Mark 3:6 And the Pharisees went forth, and straightway took counsel with the Herodians against him, how they might destroy him. Matt 12:14 Then the Pharisees went out, and held a council against him, how they might destroy him. Luke 6:11 And they were filled with madness; and communed one with another what they might do to Jesus.

The subject of Jesus healing on the Sabbath is also brought up in Luke 13:14, 14:3, and John 5:16, 9:16.