Adam Clarke on John 13:34

A new commandment I give unto you - In what sense are we to understand that this was a new commandment? Thou shalt love thy neighbor as thyself, was a positive precept of the law, Lev 19:18, and it is the very same that Christ repeats here; how then was it new? Our Lord answers this question, Even As I have loved you. Now Christ more than fulfilled the Mosaic precept; he not only loved his neighbor As himself, but he loved him More than himself, for he laid down his life for men. In this he calls upon the disciples to imitate him; to be ready on all occasions to lay down their lives for each other. This was, strictly, a new commandment: no system of morality ever prescribed any thing so pure and disinterested as this. Our blessed Lord has outdone all the moral systems in the universe in two words:

1. Love your enemies;

2. Lay down your lives for each other.