The Old Covenant proceeded through generations by blood. Fathers bore sons, sons bore grandsons, and the blood of Abraham ran in their veins. There were the commands, yes. There was the law. There was circumcision. There were the sacrifices. But we know that ultimately it was faith in the promises of God to Abraham and to his seed, his offspring born, he was explicitly told, from his own loins. The blood of Abraham was in an important sense the blood of the Old Covenant. Covenant succession was through this blood. Having lineage and descent from the patriarchs was God’s pledge and promise to fulfill his covenant to every Israelite.
But in Christ an important change took place. The blood of the Old Covenant was spilled. Christ, being a descendent of Abraham, had within himself the blood of the Old Covenant. But that blood has been shed for all men. The blood of the New Covenant is the cup of blessing in the Eucharist. Thus the lineage and descent of the New Covenant is no less by blood. We are all blood relatives in the lineage of Christ as we drink in faith. The procession of the New Covenant is no less bloody, but it has been exported. No longer bound to one human body, it has been spilled, and it is now the Church that is the body with the blood of the covenant coursing through its veins. Covenant succession is through this blood, the blood of the new covenant, shed for many. Therefore, all of you, drink of it.