Many of the things that Jesus said about the Old Testament appear to be contradictory but, fortunately, he gave us a simple overview of that law.
Jesus didn’t say anything about the New Testament.
Jesus often talked about “the law and the prophets” and “the law of Moses”. For example: “The law and the prophets were in effect until John came; since then the good news of the kingdom of God is proclaimed…” (Luke. 16:16; see also Matthew 11:12-13). This might seem to indicate that the Old Testament law no longer applied to his followers. But he also said that he was the fulfillment of the Old Testament law. “Do not think that I have come to abolish the law or the prophets; I have come not to abolish but to fulfil.” (Matthew 5:17). He then goes on to say “For truly I tell you, until heaven and earth pass away, not one letter, not one stroke of a letter, will pass from the law until all is accomplished.” (Matthew 5:17-18) Was he saying that the Old Testament law remains in force and that every command should be obeyed by Christians today? It is not clear. So what do we do with these apparently contradictory passages? Fortunately, Jesus himself gives us the answer. He said that the Old Testament law could be summed up in the two great commandments “Love God with all your heart, all your soul, all your mind and all your strength.” and “Love your neighbor the same way that you love yourself” (Matthew 22:37-40; Luke 10:27). He also introduced what we now call “The Golden Rule” and indicated that it, too, summed up the law. “In everything, do to others as you would have them do to you; for this is the law and the prophets.” (Matthew 7:12)
Jesus has authority over everything and his commands must be obeyed. At the end of Matthew’s gospel Jesus is recorded as saying that all authority in heaven and earth have been given to him. He then instructed the apostles to teach new disciples “to obey everything that I have commanded you”.(Matthew 28:18-20). So there is no question: obedience to Jesus’ teaching is more important for Christians today than attempting to keep the Old Testament law. Does God speak to us, today, through the Old Testament? Yes, of course he does. But that doesn’t mean that we have to carefully examine every word of the Old Testament and try to apply it to our lives.
Jesus didn’t say anything about the New Testament. He did say that the Holy Spirit would continue to teach his followers after he had left. “But the Advocate, the Holy Spirit, whom the Father will send in my name, will teach you everything, and remind you of all that I have said to you.” (John 14:26). However there is no suggestion, in these words, that the Holy Spirit would inspire particular people to write particular books. There is also the question as to whether these words only apply to his hearers at the time he was speaking or whether the Holy Spirit would continue to teach Jesus’ followers after the apostles had all died. This is an important point. John portrays Jesus saying these words at the last supper, which was attended by Jesus and the twelve apostles (according to Matthew, Mark and Luke). If the words “will teach you everything” apply to all Jesus’ followers through the ages, then we should expect that the Holy Spirit has been teaching Jesus’ followers new things since the times of Jesus and continues to do so today. If, however, those words only apply to those who were present at the time, then this verse cannot be used to support a claim that writings by other authors, who were not present, were inspired by the Holy Spirit. Several authors of New Testament books were not present, including Paul.