Sir, I think it is you who are "missing" it here. Christ fulfilled the Old Covenant by instituting the New Covenant...
Matthew 26:26-28 ---> "Now as they were eating, Jesus took bread, and after blessing it broke it and gave it to the disciples, and said, 'Take, eat; this is my body.' And he took a cup, and when he had given thanks he gave it to them, saying, 'Drink of it, all of you, for this is my blood of the covenant, which is poured out for many for the forgiveness of sins.'"
Mark 14:22-24 ---> "And as they were eating, he took bread, and after blessing it broke it and gave it to them, and said, 'Take; this is my body.' And he took a cup, and when he had given thanks he gave it to them, and they all drank of it. And he said to them, 'This is my blood of the covenant, which is poured out for many.'"
Luke 22:19-22 ---> "And he took bread, and when he had given thanks, he broke it and gave it to them, saying, 'This is my body, which is given for you. Do this in remembrance of me' And likewise the cup after they had eaten, saying, 'This cup that is poured out for you is the new covenant in my blood.'"
Here is Paul quoting Jesus in 1 Cor 11;23-25 ---> "For I received from the Lord what I also handed on to you, that the Lord Jesus on the night when he was betrayed took a loaf of bread, and when he had given thanks, he broke it and said, 'This is my body that is for you. Do this in remembrance of me.' In the same way he took the cup also, after supper, saying, 'This cup is the new covenant in my blood. Do this, as often as you drink it, in remembrance of me.'”
Again, it is at this moment when the new Moses, Jesus Christ, fulfills the type / figure / shadow of the old covenant of Moses in Exodus with the new reality of the Eucharistic sacrifice...
Exodus 24 (The figure) ---> The hill, the altar, the twelve, the blood, Moses, the covenant, the eating the drinking and communion with God ---> Points to the reality of the new now being fulfilled by Jesus Christ ---> The Upper Room, the altar, the twelve, the blood, the New Moses, the new covenant, the eating and drinking and communion with God.
If the Eucharist is not the body and blood of our Christ, it would be the first time in all of salvation history where the figure / type / shadow of something would have surpassed the reality of it.