The law leads us to Christ because everything in it teaches us about who he is, how to walk as he walked, and how to grow in a relationship with him, but does not lead us to Christ so that we can reject his law and go back to living in sin. In Matthew 23:23, Jesus said that faith is one of the weightier matters of the law, so obedience to it has always been about trusting God to guide us in how to rightly live and has never been about what we can accomplish through our own efforts. If God's law were His instructions for how to become self-righteous, and God does not want us to become self-righteous, then it follows that God therefore does not want to be obeyed, which is absurd, especially considering that all throughout the Bible, God wanted His people to repent and to return to obedience to His law, therefore it was not given as instructions for how to become self-righteous, but as instructions for how to express God's righteousness. Jesus is the way, the truth, and the life, and that is a life lived in obedience to the Mosaic Law, which is the same way (Jeremiah 6:16-19), truth (Psalms 119:142), and life (Matthew 19:17).
Jesus set a sinless example of how to walk in obedience to the Mosaic Law, so he would have still taught full obedience to it by example even if he had said nothing, and as his followers we are told to follow his example (1 Peter 2:21-22). Jesus began his ministry with the Gospel message to repent from our sins for the Kingdom of God is at hand (Matthew 4:17-23) and the Mosaic Law was how his audience knew what sin is, so repenting from our disobedience to it is an integral part of the Gospel of of the Kingdom and of what we need to do to enter it. Every kingdom has laws that govern the conduct of its citizens and God's law is straightforwardly the law of God's Kingdom. In Deuteronomy 4:2, it is a sin to add to or subtract from the law, and Jesus was sinless, therefore he didn't do that, but rather the sum of everything that he taught by word and by example was how to obey the Mosaic Law.