Punishment only counts as punishment when done by an authorized person. As it may apply to Christianity, who are the authorized persons? The purest version of the answer, of course, is God (Vengeance is mine, saith the Lord). Jesus, when placed in the position of judge, seemed to think no sinner qualified.
From the Gospel of John (King James Version):
8 Jesus went unto the mount of Olives.
2 And early in the morning he came again into the temple, and all the people came unto him; and he sat down, and taught them.
3 And the scribes and Pharisees brought unto him a woman taken in adultery; and when they had set her in the midst,
4 They say unto him, Master, this woman was taken in adultery, in the very act.
5 Now Moses in the law commanded us, that such should be stoned: but what sayest thou?
6 This they said, tempting him, that they might have to accuse him. But Jesus stooped down, and with his finger wrote on the ground, as though he heard them not.
7 So when they continued asking him, he lifted up himself, and said unto them, He that is without sin among you, let him first cast a stone at her.
8 And again he stooped down, and wrote on the ground.
9 And they which heard it, being convicted by their own conscience, went out one by one, beginning at the eldest, even unto the last: and Jesus was left alone, and the woman standing in the midst.
10 When Jesus had lifted up himself, and saw none but the woman, he said unto her, Woman, where are those thine accusers? hath no man condemned thee?
11 She said, No man, Lord. And Jesus said unto her, Neither do I condemn thee: go, and sin no more.
Interesting to note, Jesus also chooses not to condemn the woman, whether from his divinity and mercy or from his humanity and that he perhaps also counted himself among the sinners, I can’t say. It is clear, though, that he was saying that no sinner should be condemning anyone, even when the crime is proven – they said she was caught in the very act – and even when the punishment is traditional and acceptable to the society. It is clearly the condition of authority he finds lacking here, and lacking in everyone. He tells the woman the lesson, ‘sin no more,’ and that is the end of it.
All men are sinners, and so Jesus appears to find no adequate authority for the definition of punishment, therefore the teachings of Jesus show that only God can punish, and so when people try, it can only be abuse.