The Pharisees are simply looking for ways to accuse Jesus. They pose a practical question about healing on the Sabbath, hoping he will give the “wrong” answer.
Jesus argues once more from the lesser to the greater: if it’s ok to rescue a mere sheep, how much more ok it is to rescue a man.
The man who is healed is a bit player in this scene, a pawn of the Pharisees. But Jesus heals him and heals him perfectly. The problem was not life-threatening and could have waited for another day, but no matter.
Jesus shows that some forms of work should be permitted on the Sabbath and that the Pharisees were overly strict.
The Pharisees go off to conspire his demise. It isn’t the healing that bothers them, but rather, the teaching. In their system, he is breaking the fourth commandment and teaching his disciples to do so. He must be stopped.