The Sermon on the Mount is Jesus’ articulation of how to live the Kingdom of God. As Jesus himself said, his teaching is not a repudiation of Torah but a highlighting of those aspects of Torah that he takes to be essential. This is certainly true in this section on anger and reconciliation which is classic Jewish teaching.
For example, according to the New Revised Standard Version of the New Testament we have extant Greek manuscripts of the Gospel of Matthew that add the phrase “without cause” to the first teaching about anger: “If you are angry with a brother or sister without cause, you will be liable to judgment.” While the NRSV relegates this information to a footnote, I think it is crucial since Jesus himself gets angry in Mark 3:5 at the Pharisees’ refusal to cure on the Sabbath, and again in Matthew 21:12 when he drives the money changers out of the Temple. Both instances are clearly in line with the righteous anger of the Hebrew Prophets.
As for Jesus’ condemnation of calling people “fools,” something Jesus himself does twice (Matthew 23:17; Luke 11:40), a fact that I find humanizing and endearing, here, again, Jesus is citing established Jewish teaching.
The Book of Proverbs says, “A fool always loses his temper, but the wise man holds back,” (Proverbs 29:11); and “A fool’s wrath is known at once,” (Proverbs 12:16). Proverbs also tells us that anger is the source of terrible strife (29:22; 30:33), and Psalm 37:8 urges us to “cease from anger” because it only causes harm. Jesus listeners, familiar with these and other Jewish teachings warning against anger, would not find Jesus’ teaching surprising at all. Even Jesus’ equating of anger with murder is part of Pharisaic teaching: “Whoever shames another in public is like one who sheds blood,” (Bava Metzia 58b).
When elevating reconciliation over sacrifice Jesus is drawing on Leviticus 6:1-7 where God says that if people have sinned against their neighbor they must first make that right and then offer a sacrifice to God. The Pharisees even had procedures for what to do with a sacrifice that has to be postponed.
Jesus’ final teaching regarding the two plaintiffs going to court over some dispute is also standard Pharisaic teaching. Jesus directs this comments to the guilty party since he urges this person to “pay the last penny.” In tractate Sanhedrin 95b of the Talmud the rabbis make the same assumption and urge an out of court settlement. It is likely that both they and Jesus are drawing on an even older teaching in the Book of Proverbs that, again speaking to the guilty, says “Do not go hastily to court,” (Proverbs 25:8).
The Hebrew Bible, the Pharisees, and Jesus are all saying the same thing: anger is dangerous, reconciliation with others takes precedent over prayer and sacrifice, and trying to avoid responsibility for one’s actions by going to court is a bad idea. The Way of Jesus is the Way of Torah pared, in good prophetic style, to the ethical core.