In the Letter of Paul to the Romans, Paul is making his strongest argument for the case that the old ways no longer apply. The following of the Jewish rabbinical laws and traditions has been superseded by the example and teachings of Jesus, and what Jesus taught was that the way to God was through faith in God and the acceptance of the guidance provided through the Holy Spirit.
For the law of the Spirit of life in Christ Jesus has set me free from the law of sin and death. (Romans 8:2, RSV)
Paul goes on to explain that believers have a new set of standards by which they should structure their lives - the expectations set by the Spirit. Those who live according to the law, which Paul equates with living "according to the flesh" (Romans 8:5), are living into patterns based on sin and separation from the will of God. Those who "submit to God's law" (Romans 8:7) will be united with God and Jesus, through the power of the Holy Spirit.
In this chapter of his letter to the Romans, Paul is once again arguing for the supremacy of faith in God and acceptance of the spirit of God. He is saying that this is what people should turn to instead of trying to follow the law.
Paul argues that the law is a worldly thing; a thing of "the flesh." He says, essentially, that it is a man-made corruption of what God really wants. Paul argues that relying on the law is relying on earthly things. This is dangerous because these things can be corrupted. Instead, Paul says, Christians should try to reach the "realm of the spirit." He wants Christians to seek guidance from the Spirit instead of from the laws of man.