Jesus explained it this way:
21Jesus answered and said unto them, I have done one work, and ye all marvel. 22Moses therefore gave unto you circumcision; (not because it is of Moses, but of the fathers;) and ye on the sabbath day circumcise a man. 23If a man on the sabbath day receive circumcision, that the law of Moses should not be broken; are ye angry at me, because I have made a man every whit whole on the sabbath day?
Notice Jesus' contrast: they are willing to chop off part of a person's body on the Sabbath, but they did not want Jesus restoring a man's body on the same day (recall that Jesus healed on the Sabbath day in John 5). That's counterintuitive: if they are willing to do harm to flesh on the Lord's Day because it was necessary to obey the Mosaic law, why should they be opposed to Jesus restoring flesh on the same day?