What does Luke 6:6 mean?
Luke records a second altercation Jesus has with the Pharisees about what is allowed on the Sabbath. They first clashed over the appropriateness of picking grain and eating the kernels (Luke 6:1–5). This second is similar in that it also deals with a human need on a day that Jews are supposed to refrain from work.The Mosaic law is clear that Israelites/Jews were not to do work on the Sabbath (Exodus 31:12–17). The law was so serious that a man was executed for picking up sticks in defiance of this rule (Numbers 15:32–36). Ignoring the Sabbath was a primary reason God judged and disciplined the Israelites (Ezekiel 20:13). God lists it on par with shedding blood, abusing refugees, and adultery, and gives it as a reason for the Babylonian captivity (Ezekiel 22:6–15).
After the Jews returned from Babylon, the scribes feared the people's sin would cause God to exile them again, so they made extra-biblical regulations to provide specific parameters. The Pharisees feel it is their responsibility to make sure everyone follows those regulations. They have extra incentive now: if they can catch Jesus breaking the regulations, they may have an opportunity to get rid of Him (Luke 6:7, 11).
"Withered" means to be shrunken and immobile. It's possible the man's arm is paralyzed, leading to muscle atrophy.