Thank you for the question on reconciling the teaching of Jesus and the teaching of Paul, “How do you reconcile Paul’s teachings with Matthew 5:18?”
As one reads a Bible verse, may I encourage readers to read the context so that the verse could be understood properly.
Jesus said this, “ “Do not think that I have come to abolish the Law or the Prophets; I have not come to abolish them but to fulfill them. 18 For truly I tell you, until heaven and earth disappear, not the smallest letter, not the least stroke of a pen, will by any means disappear from the Law until everything is accomplished. 19 Therefore anyone who sets aside one of the least of these commands and teaches others accordingly will be called least in the kingdom of heaven, but whoever practices and teaches these commands will be called great in the kingdom of heaven. 20 For I tell you that unless your righteousness surpasses that of the Pharisees and the teachers of the law, you will certainly not enter the kingdom of heaven” (A searchable online Bible in over 150 versions and 50 languages). Bible citations are from the New International Version.
Here is my reconciliation between Jesus and Paul’s words:
A. Jesus declared that he came to fulfill the Sacrificial Law (vs. 17).
Jesus fulfilled the sacrificial Law of reconciling Jews and later the non-Jews to God through his atoning death. John the Baptist declared that he is the Lamb of God who takes away the sins of the world (John 1:36). Jesus’ death as the sinless Lamb of God was to atone for sins (John 10:11, I John 2:2).
The Apostle Paul says this concerning the atoning work of Jesus Christ. “For what the Law could not do, weak as it was through the flesh, God did: sending His own Son in the likeness of sinful flesh and as an offering for sin, He condemned sin in the flesh, 4 so that the requirement of the Law might be fulfilled in us, who do not walk according to the flesh but according to the Spirit” (NIV). See also Ephesians 2:14–18.
The immediate fulfillment of the Law is the reconciliation between God and humans for through the Law no human being can be righteous before God. (Rom. 3:23). Jesus is The Way, The Truth, and The Life to God.
B. Jesus declared that he will fulfill the Kingdom Law (vs. 18).
Jesus states that every letter of the Law will be fulfilled. The question becomes the timing of when the Law will be fulfilled. The Law prophesied of a coming prophet whom the people must listen to him. This prophet is viewed as the Messiah who would inaugurate the Kingdom of God.
Deuteronomy 18 says this, “The nations you will dispossess listen to those who practice sorcery or divination. But as for you, the LORD your God has not permitted you to do so. 15 The LORD your God will raise up for you a prophet like me from among you, from your fellow Israelites. You must listen to him. 16 For this is what you asked of the LORD your God at Horeb on the day of the assembly when you said, “Let us not hear the voice of the LORD our God nor see this great fire anymore, or we will die.” 17 The LORD said to me: “What they say is good. 18 I will raise up for them a prophet like you from among their fellow Israelites, and I will put my words in his mouth. He will tell them everything I command him. 19 I myself will call to account anyone who does not listen to my words that the prophet speaks in my name. 20 But a prophet who presumes to speak in my name anything I have not commanded, or a prophet who speaks in the name of other gods, is to be put to death.”
Jesus is that Prophet, the one who speaks the very words of God. He is the Word, the Logos who spoke the very words of God and did the very acts of God.
Acts 9, the Apostle Paul declares that Jesus is the Christ or the Messiah. He says, “ But Saul kept increasing in strength and confounding the Jews who lived at Damascus by proving that this Jesus is the Christ.”
Jesus further states that kingdom people will obey his teachings which he further elaborates on the Sermon of the Mount. The context in my viewpoint is that Kingdom people do not live by the letter of the Law but by the power of the Holy Spirit. Those who lived by the Spirit of God will fulfill the spirit of the Law and not just the letter of the Law. Paul says this in Galatians 5 that the display of the fruit of the Spirit in which there is no law, “Against such things there is no law.”
The letters of the Apostle Paul does complements the words of Jesus.
For more perspectives:
https://www.quora.com/How-do-you-reconcile-Pauls-teachings-with-Matthew-5-18