Both Jesus and Moses agreed that murder is a sin against God and will deserve punishment, but Jesus does not stop there.  Jesus looks deeper into the psyche of men and teaches us that anger and hatred lie beneath the act of murder itself.  Anger and hatred are the emotions that become manifest in violent acts such as murder.  The act of murder is considered to be a crime against society, but in the kingdom of Heaven it is the root causes, anger and hatred, which are the sins against God.  These are the real sins of men—the act of murder is an expression of the hatred and anger of man’s spirit.  

Jesus continues to teach that even speaking against your brother in the form of insults or name-calling could also put one’s spirit in jeopardy. This basic lesson is reflected in the teachings of Paul:

Romans 12:17-18 (NKJV)
¹⁷Repay no one evil for evil. Have regard for good things in the sight of all men.
¹⁸If it is possible, as much as depends on you, live peaceably with all men.

We have to strive for peace if we are to have peace.  This ties directly into the Beatitudes where the peacemakers are blessed because they are the children of God. So inner peace begins when we make peace with our brothers.