What Is Sin Under the New Covenant?

There is a difference between following the rules of a book, such as the scroll containing the Law of Moses, and obeying the will of the risen Christ. The first is the old covenant. The second is the new covenant; although we have to obey the teachings of the Apostle until we are able to recognize the voice of the Lord Jesus.
The two most destructive forces in the Christian churches, and also in the world, are sin and self-will. These two forces interact. For anyone to be saved into the Presence of Christ, these forces must be overcome!
It may be true that there are few things as confusing as is true of Christian thinking concerning sin. Paul emphasized that we are not under the Law of Moses but under "grace," whatever that may be.
Unless we define "grace" as God's Presence in Christ to accomplish God's will, and use it instead as an excuse for our sinning, we will frustrate the purpose of the new covenant.
The new covenant was given to us because the Israelites were not able to satisfy God's desire that people behave righteously.
It will not be like the covenant I made with their ancestors when I took them by the hand to lead them out of Egypt, because they did not remain faithful to my covenant, and I turned away from them, declares the Lord. (Hebrews 8:9)
Now, do we honestly believe that God decided human beings would always be unable to act in His image and gave "grace" as an excuse for their behavior? Would this be a better covenant from God's point of view?