Quoting the false to prove the Truth. Why?
If someone makes an historical claim about what the prevalent view of the Pharisees, then the Talmud can be used as a valid source to support to reject that claim regardless of whether or not we agree with whether that view is correct.
You refer to the Talmud as false, so is it your belief that we should disagree with every last thing taught by the Talmud is false? If the average Christian were to actually read the Talmud, then while there would be things that they disagreed with, they would nevertheless find much that they would agree with, especially when there are number of things taught in the Talmud that are identical to what Jesus taught, so we can think that some or many of the things taught in the Talmud are false without disagreeing with everything in it. The Talmud discusses how to interpret the Torah and it would be a stretch to think they so thoroughly misunderstood the Torah that they got every last interpretation wrong, but rather there are many interpretation that the average Christian could agree with. A Christian could even disagree with whether a command should be obeyed while grant that the Talmud expresses a correct understanding of how to obey that command. As an individual, there is much of value that I can learn from someone even if there are many important things that I strongly disagree with them about. People should first know what is taught by the Talmud before they consider it to be false.
And it seems to me that the traditions of the Pharisees IS the talmud of Babylon. Ιησους doesn't favor "teaching for doctrine the commandments of men."
In Deuteronomy 17:8-13, it gives the basis for giving men the authority to making rulings about how to correctly obey the Torah. When someone tries to put the Torah into practice, then there are many questions that naturally arise. For example, in Numbers 15:38, it commands to wear tassels on the corners of our garments, with a thread of blue on the tassel of each corner. However, it doesn't say how long these tassels should be, how to attach them to the corners of our garments, how many knots should be tied, what shade of blue to use, what to use to make the pigment, what other colors should be used, what to do if our garments don't have corners, and so forth, so all of these things got left up to tradition, and there is nothing inherently wrong with following them. Jesus followed this command and no one is recorded for criticizing him for how he wore them.
Likewise, in Leviticus 19:23-25, it commands that when they enter the land that they should eat the fruit of a tree in the first three years after it has been planted, on the fourth it is holy to the Lord, and on the fifth year they were free to eat of it. So what should be done if a tree is planed on a hill and the fruit rolls down the hill and mixes with the fruit of a tree planted in a previous year? Someone had to make that ruling and it got passed down as case law, and while we are free to agree or disagree about whether they made a correct ruling, we should not consider their ruling to be false before we know what ruling they made.
"Beware the leaven of the Pharisees" still rings out from Heaven. The only pure words are the loaves themselves, not the bushels of crumbs via commentaries.
In Luke 12:1, it directly states that the leaven of the Pharisees is hypocrisy. Just because someone is being hypocritical does not necessarily mean that they are wrong about what we should be doing, just that their actions are for show. In Matthew 23:23, Jesus said that the Pharisees were hypocrites and that tithing dill, mint, and cumin was something that they ought to be doing while not neglecting weightier matters of the Torah of justice, mercy, and faithfulness, so he affirmed that what they were doing what they ought to be doing, but was calling them to a fuller obedience to the Torah in a manner that was in accordance with its weightier matters and free from hypocrisy. In Matthew 23:2-4, Jesus said that the Pharisees sit in the seat of Moses, so do whatever they tell you, but not as you do, so he recognized their authority, but warned against their hypocrisy.
People keep saying that Ιησους kept the commandments of Moses... and I'm always left thinking: why would God the Son have to follow what any man said? Because no matter how pure was the man being followed, the man's alphabet itself cannot improve the words of the Father. And unless the words of Moses were never changed, and no part ever written for those with hard hearts...
In Deuteronomy 5:31-33, Moses wrote down everything that God commanded without departing from it, so all of the Law of Moses is the Law of God, and it is referred to as such in verses like Nehemiah 8:1-8, Ezra 7:6-12, and Luke 2:22-23.
Well, Deuteronomy 18:18-19, John 12:48-50, John 7:16-17, John 17:6-8 say Ιησους words came from the Father, and Matthew 21:37 shows Him seeking the fruits that the Reign of God produces... last of all He sent His Son.
The same God who gave the law to Moses also sent Jesus to spent his ministry showing us how to obey it by word and by example, so there is no disagreement.
Now, some gentiles are pretending that the Kingdom of God comes to them... forgetting entirely that Matthew 9:35-38 shows the that fields in which Ιησους was speaking were white with harvest (fruits of the kingdom). So that, when the 12 Disciples were sent only unto the Lost Sheep of the House of Israel (Matthew 10:5-7), they were gathering these fruits of the Kingdom of God. So the Kingdom of God was given to the nation producing the fruits thereof... the House of Israel is that nation.
So the Kingdom of God was taken from the House of Judah/Jerusalem and given to the House of Israel... just as the Kingdom was taken from Judah at Solomon's divided kingdom.
In Romans 4:9-12, Abraham is the father of both circumcised and the uncircumcised who walk in the footsteps of faith, so the promises of the Kingdom are not just for Jews, but for Gentiles too. Gentiles who repent and bear the fruit of the Kingdom through faith in the promise are citizens of the Kingdom. Again, Abraham spread the Gospel to the nations before there were any Jews, so it could not be limited to them. Again, Galatians 3:26-29 connects both Gospels by equating those who are children of God through faith in Christ with those who are children of Abraham, heirs to the promise. Furthermore, Jews were given the role of being a light to the nations and the Gospel went out to the Jew first and then to the nations so that Jews could have the opportunity to fulfill this role (Romans 1:16).