Love does no wrong to a neighbor; therefore love is the fulfilling of the law. (ESV)
We read this verse and at first it seems very liberating. We can fulfill the law by simply choosing not to do any wrong to our neighbor. In fact, I have spoken to people who will go so far as to make the claim that they have never done anything to hurt anybody. They are confident that this is all that is required to fulfill God's Law.
First of all, the sad reality is that according to God's righteous and holy standard we all stand condemned by our very nature, regardless of anything we have actually done. In our nature, we have a desire to please ourselves above any other, including God. So, before we even get to the question of whether it is possible to keep from doing wrong to our neighbor, we are lawbreakers by nature.
Now, let's consider whether or not one can make the claim that they do not do any wrong to their neighbor. There were Jews, the Pharisees in particular, who thought they were doing pretty good at keeping the Law. In the Sermon on the Mount Jesus shows just how far from God's holy standard we all are. The Pharisees were not even close to holiness.
Jesus came and said, "You have heard it said, but I tell you. . ." He was letting them know that if they thought they were obeying the Law they were not even close. Those who were confident that they had not committed murder Jesus says, "If you hate someone in your heart, you are a murderer." He lists all kinds of behaviors that expose us for the lawbreakers that we are by nature.
There is only one solution for us. We need a new nature. That only comes by faith in Jesus Christ. We confess our sin. He forgives us and gives us a new nature. He lives his holy life through us. Are you trying to fulfill the Law? Stop. Allow the Lord to live though you. He is holy. He can do it.