Jesus is not changing the Law of Moses. He is explaining it. Our righteousness is no better if we seek to worship ever so correctly while holding ill will toward another or while being the cause of alienation. He was explaining the meaning of it. Pharisaic rightness conformed to the outward requirement.
True righteousness begins in the heart.
Jesus' answer indicated that God did not give a man a checklist of fouls to keep against his wife so he could throw her out. From the beginning it was not so. God made an exception under Moses because of the hardness of man's heart. Sexual unchastity destroys the basis of marriage. Jesus recognized that.