Assuming the more difficult textual reading in Mark 1:40-45, Jesus is angry when a leprous man comes in faith to be healed.
Graham Twelftree suggests:
“Indeed, it could be that Mark intends the righteous anger to be directed at the forces of evil for having distorted one of God’s creatures. Or it could be that Jesus is angry at the injustice done to the lepers by Israel. Or Jesus may be responding angrily to people for breaking a divine sanction…. the next part of the story favors the suggestion that Jesus may have been angry over a breach of the law [that is, the leprous man was breaking the law for approaching Jesus while unclean].” Jesus the Miracle Worker, 62.
To me, Twelftree’s suggestion doesn’t fit comfortably with what Mark is doing with the story: The action of the leprous man is exactly the sort of thing that Mark wants to commend: coming to Jesus with an acknowledgement of need, and faith that Jesus will meet that need. Furthermore, Jesus is not presented as reluctantly conceding to an annoying lawbreaker – on the contrary, he explicitly says, “I am willing.”
So why is Jesus “angry” when he is asked for cleansing?? I’ve just been pondering this with colleague Marty. I think that perhaps the best explanation is that – as in Mark’s later story of the withering of the figtree – Jesus is angry that Israel’s temple/priesthood is not bringing the fruit of cleansing that it ought to be bringing. So after healing this man, Jesus sternly warns him not to be sidetracked, but to go directly to the temple and present an offering for his cleansing, “as a testimony to them.” As in the subsequent several stories in Mark’s Gospel (up to 3:6), Jesus is sending a message to the would-be leaders of Israel:
See, I am sending my messenger to prepare the way before me, and the Lord whom you seek will suddenly come to his temple. The messenger of the covenant in whom you delight – indeed, he is coming, says the Lord of hosts. But who can endure the day of his coming, and who can stand when he appears? (Malachi 3:1-2)