Jesus fulfilled the old law of Moses by the perfect sinless life that He lived, and He then "nailed it to the cross" (Col. 2:14) when He died the sacrificial death on Calvary for all of mankind. The law of Moses was then replaced by Jesus becoming the "Mediator of a better covenant, which was established on better promises" (Heb. 8:6). One of the many things that is "better" about the New Covenant, is that it ushered in the new morality of Jesus Christ. The morality that Jesus would teach all men to live by was very much superior to that of the Old Testament.
The Law of Moses was given to the children of Israel for two primary reasons. First, the law was needed to separate the Jewish people from the gentile world in order to protect the seed line of the coming Messiah. Secondly, the law was to make known and define sin for the people. The Apostle Paul said, "I would have not known sin except through the law" (Rom. 7:7). The law of Moses served as a "schoolmaster" or "tutor to bring us to Christ" (Gal. 3:24). Paul further defines the purpose of the law when he said it was "added because of transgression till the Seed (Christ) should come to whom the promise was made" (Gal. 3:19). The Old Covenant required a strict carnal legal system of rules to maintain the state of separation God expected for the Jewish people. It gave specific commands and rules that were not to be broken, and if they were broken the punishment was to be handed out immediately. The laws dealt with external actions, but not the internal motives for those actions.
The New Covenant of Jesus took things to the next step, which is why it was so much "better" than the old. The morality of Jesus would look to the very heart of what drove man to commit the sins that where violations of the law. The law of Moses would give commandments such as do not commit murder, or do not commit adultery. The morality of Jesus goes further and says do not have anger or lust in your hearts which would lead you to committing murder or adultery. People under the old law were told not to violate the laws because of the strict and immediate punishment that would follow. The morality of Jesus says we do not even think in our hearts to do such things because of the love we have for God and our fellow man.
The basis for the morality of Jesus can be found in the answer he gave to a man who ask him what the greatest commandment was. He said, "thou shalt love the Lord thy God with all thy heart, and with all thy soul, and with all thy mind. This is the great and first commandment. And a second, like unto it is this, thou shalt love thy neighbor as thyself" (Matt. 22:37-39). Everything starts first with our love for God, and then secondly, our love for our fellow man. Jesus understood that what a man says and does is based on the condition of that man's heart. The morality of Jesus goes straight to the heart of man showing that the motives for why we do things is what is really important. King Solomon said, "for as he thinketh in his heart, so is he" (Prov. 23:7). Jesus said, "for out of the heart proceed evil thoughts, murders, adulteries, fornications, thefts, false witness, blasphemies" (Matt. 15:19).
Jesus wants His followers to do the things they do because of the love they have in their hearts for God and for man. He wants disciples who obey Him because they love him. He said, "If you love me, keep My commandments" (John 14:15). -Ed