Jesus’s main critique of the Pharisees was that they were substituting God’s law with man-made traditions. The Pharisees were scapegoating laws in the old testament by reinterpreting certain verses, and these modifications are preserved in the Talmud. For example, they interpreted Deut 24:1 to allow for “any cause” divorce or adding “hate you enemies” to love your neighbor in Lev 19:18. Jesus of course corrected them in Matt chapter 5:31-32 & 5:43-48, as well as Matt 19 & Luke 10:25-37. Jesus often pointed out the fact that the Talmud (commentary on the Torah) was heresy since it contradicts the Torah.
In Mark 7:6-8 (as well as Matthew 15:1-20) the Sanhedrin council criticizes Jesus and his disciples for not doing “ritual handwashing” before eating. He says, “Isaiah was right when he prophesied about you, for he wrote, ‘These people honor me with their lips, but their hearts are far from me. 7 Their worship is a farce, for they teach man-made ideas as commands from God.’”[Isa 29:13] In verse 8 he says they ignored God’s law and substituted it with their own tradition. In verses 9-13 he gives specific examples of them using the Law to put tradition over love.
The Netilat Yadayim or “ritual handwashing”, has nothing to do with hygiene, it is a custom that comes from the oral tradition of the Pharisees and is only written in the Talmud, NOT in the Tanakh (old testament). This is why Jesus doesn’t observe it, because it never came from God in the first place. You can learn more about that here.
The Talmud on divorce:
“…And Beit Hillel says: He may divorce her even due to a minor issue, e.g., because she burned or over-salted his dish, as it is stated: “Because he has found some unseemly matter in her,” meaning that he found any type of shortcoming in her. Rabbi Akiva says: He may divorce her even if he found another woman who is better looking than her and wishes to marry her, as it is stated in that verse: “And it comes to pass, if she finds no favor in his eyes.” (Talmud: ‘Gittin,’ 9:10) Beit Hillel or Hillel the elder, was the grandfather of that Gamaliel. Gamaliel is mentioned in Acts 5:34-40, and he is the teacher of Paul the Apostle according to Acts 22:3.
In Matthew 5:31-32, and Matt 19:9 Jesus affirms the law of divorce from the Torah. The Pharisees came up with ‘any cause’ divorce, to allow them to divorce for any reason. The Torah only allows divorce for “uncleanness” or indecency, which likely refers to some kind of wickedness like badmouthing or attempting to poison her husband or committing adultery, etc (Deut 24:1), and abuse of a spouse via neglect of food, clothing, and sex (Ex 21:10-11). Jesus calls out the scapegoating of adultery by saying that it counts as adultery if you lust after another woman in your heart (Mt 5:27- 30). Therefore, it still counts as adultery even if a man gets a divorce and then remarries a new woman because the reason why the man got the divorce was driven by lust in his heart, not because his spouse broke the covenant.
Other examples of Jesus’ affirmation of the law:
Against murder and applies its principles by saying that if murder that arises from hatred is wrong, then murderous hatred is also wrong (Mt 5:21-26). Against making false oaths to God, saying that if it is wrong to lie to God, then it is wrong to speak any lies (Mt 5:33-37). Against revenge by saying that if the law tells us to restrict our wish for revenge, then we should avoid revenge altogether (Mt 5:38-42).
Jesus says the 2nd greatest command is to love your neighbor from Lev 18:19, but he rejects the words “and hate your enemy,” which some people had added to this command by the time of Jesus (Mt 5:43-47).” The Torah even says to love you, enemy, by returning his ox to his neighbor in Ex 23:4. Surely if the Torah requires one to help an enemy’s livestock then they are expected to help an enemy’s servant, child, spouse in need, and even the enemy themselves, and return anything living or nonliving to an enemy when lost. The Good Samaritan parable in Luke 10:25-37 was presented by Jesus when explaining to Pharisees that loving your neighbor includes your enemies. This was after they asked him what the two greatest commandments were and Jesus replied loving God (the Shema) and loving your neighbor. (Deut 6:5; Lev 19:18) The Jews and Samaritans didn’t get along and had culture clashes, so Jesus called out the religious leaders’ hypocrisy, by giving an illustration of a Samaritan (an enemy) who treats Jews better than Jewish leaders treat their own, and in that scenario, he would be counted as righteous for keeping the Torah.