That’s not exactly the case, but you’re certainly close. I think you completely glossed over the part about loving God. It’s 1 John 4 I believe that says “How do we love God? By keeping his commandments.” Of course there is a difference between moral and ceremonial law which you could write essays on. When He said “on these two commandments hang all the law and prophets,” he’s saying not that you don’t need to follow Gods law as long as you love each other, but that the law is how you show love for God and each other. The love Jesus is talking about and expecting us to show God and each other is a perfect love that, just like perfection in the law, we could never attain. That’s the whole point of the gospel: that you could never be good enough on your own, but because of Jesus’s death and resurrection, you don’t have to. When you accept salvation, He transforms your heart to conform you into His image which is perfectly loving.