I believe He’s right. Jesus clarified & transfigured the teachings of the Old Testament. As God the Son, the 2nd Person of the Holy Trinity, He had the right to create a New Covenant. That He did. And, I’m glad for it!
I would ask you how would answer your own question in light of Scripture, where Jesus plainly tells us in Luke 22:20 that “…This cup is the new covenant in my blood, which is poured out for you.”
The Council of Jerusalem in Acts 15 NABRE-USCCB: http://www.usccb.org/bible/acts/15
Where St. Paul states in 1 Corinthians 11 (BibleHub): 23For I received from the Lord what I also passed on to you: The Lord Jesus, on the night he was betrayed, took bread, 24and when he had given thanks, he broke it and said, “This is my body, which is for you; do this in remembrance of me.” 25In the same way, after supper he took the cup, saying, “This cup is the new covenant in my blood; do this, whenever you drink it, in remembrance of me.” 26For whenever you eat this bread and drink this cup, you proclaim the Lord’s death until he comes.
27 So then, whoever eats the bread or drinks the cup of the Lord in an unworthy manner will be guilty of sinning against the body and blood of the Lord. 28 Everyone ought to examine themselves before they eat of the bread and drink from the cup. 29 For those who eat and drink without discerning the body of Christ eat and drink judgment on themselves. 30 That is why many among you are weak and sick, and a number of you have fallen asleep. 31 But if we were more discerning with regard to ourselves, we would not come under such judgment. 32 Nevertheless, when we are judged in this way by the Lord, we are being disciplined so that we will not be finally condemned with the world.
From Colossians 2 NABRE-USCCB:
You were buried with him in baptism, in which you were also raised with him through faith in the power of God, who raised him from the dead.
And even when you were dead [in] transgressions and the uncircumcision of your flesh, he brought you to life along with him, having forgiven us all our transgressions;
obliterating the bond against us, with its legal claims, which was opposed to us, he also removed it from our midst, nailing it to the cross;
despoiling the principalities and the powers, he made a public spectacle of them,l leading them away in triumph by it.