Matthew’s Gospel was written by followers of Matthew.
Thirty years after the death and Resurrection of Jesus, Jewish terrorists began hiding on roadsides, then ambushing Roman soldiers. The terrorists would then hide in alleyways deep in Jerusalem where the Romans could not get at them.
The Romans, after losing many men over three years, made the fatal decision of closing off Jerusalem, then killing all the inhabitants, and destroying the city.
When the Romans had locked the gates, and after they had erected catapults to hurl fire into the city, they were approached by a delegation. It was the Pharisees who had always been loyal to Rome; and the Roman General Titus allowed them to leave the doomed city.
Those Pharisees set up camp on the Mediterranean coast, and from there they followed news of the temple and the city’s complete destruction.
As orthodox Jews they had always identified themselves as people of the Temple, so on losing the Temple, they were left without a core to their religion. After pondering the matter, they decided that what made them real Jews was their following the thousands of extra laws their rabbis had added to the Law of Moses.
After firmly deciding on that, they looked around, and they found that half of the Jewish population was made up of followers of that Jesus who had scoffed at those precepts added to the Law of Moses.
Those leading Pharisees then announced that the followers of Jesus had lost their right to be called Jews. They were saying that Jesus had meant to destroy the Law and the Prophets.
Matthew wrote his Gospel to prove that the opposite of that was true. He quoted Jesus saying, “I have not come to destroy the Law and the Prophets. I have rather come to fulfill them”
Matthew quoted the way that Jesus in his Sermon on the Mount, one by one completed the Law of Moses. Where Moses had said “Thou shalt not kill,” Jesus said, “You should not be angry with your brother.” Where Moses had said, “Thou shalt not commit adultery,” Jesus had said, “You shall not lust.”