The Scribes and Pharisees would have been good neighbors if they lived next door. They wouldn't have thrown wild parties. They would have spoken against abortion and the perversion of the marriage bed by fornication and homosexuality. And they gave to the work of the church. But their righteousness could not get them into the Kingdom of Heaven. Jesus teaches Christians that our righteousness must be even better than this. But how can this be? It is impossible with us. But Christ came to fulfill it for us. He therefore declares us to be the light of the world. He declares us to be sons of God. He declares us righteous before the throne of God. And after doing this, He teaches us about this righteousness.
The righteousness that Jesus teaches us is not a righteousness that places itself above our neighbor, but one that seeks reconciliation with Him. The righteousness that Jesus teaches us is one that seeks out peace and carries out kindness. This is what Jesus sought when He fulfilled all righteousness by His own obedience under the law (Matthew 3:15; Philipians 2:5-11;
Romans 5:18-19). He sought our salvation. St. Paul says that God demonstrated His righteousness by giving His Son to die for our sins (Romans 3:25-26). God saves us by His righteousness.
He reconciles us back to himself. Therefore, Jesus teaches us, as children of God who are righteous through faith in his saving death, what it means to live in righteousness. He credits us with His own righteousness, and then He admonishes us to pursue in our lives what is already ours by faith. He teaches us, as St. Paul says, to present our members to God as instruments of righteousness. And why? Because "sin will have no dominion over you, since you are not under the law but under grace. (Romans 6:13-14)" As God has reconciled us to himself, Jesus teaches us to be reconciled with one another. He teaches us a greater righteousness, which is not formed by our own adherence to the law, but by the mercy of our gracious God who seeks out and establishes peace.