Moses went up Mount Sinai and received from God the Ten Commandments. Jesus goes up the mountain of the beatitudes and give the New Law. What we heard said of old was the voice of Moses. What we hear today is the voice of Jesus. It is new. It is different. Jesus raises the bar in our effort to live holy lives. More is expected from disciples of Jesus!
Most of us do not commit murder. It is not so easy to control our anger and be a peacemaker. See the difference between the Old and the New! Jesus teaches ideals that we always seek but never fully reach. He teaches us to rely on the Holy Spirit.
Likewise, most of us do not commit adultery. Jesus commands purity of heart. We all know that adultery in our heart is a violation of the New Law of Jesus. Jesus demands higher standards. He is the new Moses. his teaching is for disciples, those who have gone up the hill to be taught by Jesus.