Some say these verses show that Jesus added to God’s law and that what he commanded was new in the sense of being an original directive. This cannot be the case because adding to God’s law is a violation of his law. 

“Do not add to what I command you and do not subtract from it, but keep the commands of the LORD your God that I give you.” (Deuteronomy 4:2)

Also, loving neighbor as self was one of the most important laws established by God through Moses.

“You shall not take vengeance or bear a grudge against the sons of your own people, but you shall love your neighbor as yourself: I am the LORD.” (Leviticus 19:18)

Instead, Jesus was expounding on (making full) the law they already knew. He was adding new *nuance* to their understanding in the same way he pointed out that being angry was the same as murder and lusting was the same as adultery. He was instructing them to love one another (a long established law) just as he had loved them – meaning in a way that no one had ever experienced until he came and showed them grace upon grace (John 1:16).