Bringing The Law Down the Hill...
In Matthew, the teachings to come... are delivered "on the mountain"; but here Jesus comes down from there with his new "laws".
Two related things going on here: Jesus implying that he is the divinely authorized King of Israel (Jesus citing the precedent of David, anointed King but still on the run from Saul's partisans, bending sacred regulations in case of need. Jesus appointing twelve of his followers as "apostles", 'disciples' in the other gospels except that here we have an emphasis on them as "messengers" or "missionaries", the role they are to take up after Jesus' death. But the basic reason for choosing precisely 12 is that they match the number of tribes that traditionally make up Israel. In Mark we find them avidly discussing who is to get the best place when Jesus takes power and they can start 'judging Israel' from their 12 thrones.) And Jesus delivering the terms of a new Covenant, ala Moses.
As Wright points out, Pharisees were unlikely to make too much fuss over one individual Jew shading one of 600+ Commandments-- but when that Jew is a Messianic candidate, possessed of evident spiritual power and great personal charisma, everything that he and his closest followers do is a matter of concern.
This man is a great prophet, possibly the Messiah-- or he has a covenant with Beelzebub and is leading Israel astray, in which case finding an occasion to kill him looks like their plain duty: "If a prophet arises among you, or a dreamer of dreams, and gives you a sign or a wonder, and the sign or wonder which he tells you comes to pass, and if he says, 'Let us go after other gods,' which you have not known, 'and let us serve them,' you shall not listen to the words of that prophet or to that dreamer of dreams, for the Lord your God is testing you... That prophet or that dreamer shall be put to death, because he has taught rebellion against the Lord your God, who brought you out of the land of Egypt and redeemed you out of the house of bondage, to make you leave the way in which the Lord your God commanded you to walk." [from Deuteronomy 13].
So where does a difference of interpretation... not that far from what the rabbis eventually decide about the Sabbath (that it should be violated in cases where human life is at stake) become an outright incitement to rebellion against the commandments? Can one establish a "new covenant"?-- without raising questions about the Covenant one has? This is not the "Jesus" of John's gospel... but the claims he is implying, by everything he says and does, are putting his rabbinic critics on the spot. If he isn't in fact the Messiah, he is a very dangerous man, and not one they're allowed to indulge.
Coming next: the laws of this new deal.