Jesus/Torah: what he opposed: sabbath

Examples of what Jesus opposed in Torah:

Mark 2:23-28

"One Sabbath Jesus was going through the grainfields, and as his disciples walked along, they began to pick some heads of grain. 24The Pharisees said to him, "Look, why are they doing what is unlawful on the Sabbath?"
25He answered, "Have you never read what David did when he and his companions were hungry and in need? 26In the days of Abiathar the high priest, he entered the house of God and ate the consecrated bread, which is lawful only for priests to eat. And he also gave some to his companions."

27Then he said to them, "The Sabbath was made for man, not man for the Sabbath. 28So the Son of Man is Lord even of the Sabbath." "

Line 27 is the key. In Torah keeping the Sabbath is one of the 10 Commandments:

Exodus 20:10
"but the seventh day is a Sabbath to the LORD your God. On it you shall not do any work, neither you, nor your son or daughter, nor your manservant or maidservant, nor your animals, nor the alien within your gates."

Here Jesus wants to reinterpret the rules for keeping the Sabbath. His first statement, line 27, that sabbath is for man and not the other way around, implies that we can define how we keep the sabbath. Line 28 indicates that in particular, he, Jesus can determine how to keep the sabbath.

The key part of the commandment is "you shall do no work." Now how do we define "work"? In the story Jesus was obviously violating the standard interpretation -- that's why the pharisees were objecting to his behavior.

Why doe Jesus propose this new interpretation?