While I strongly disagree with his attempt to defend the Mass as a propitiatory sacrifice and the dogmatic understanding of the nature of “Real Presence” (i.e., Transubstantiation [for more on this, see Responses to Robert Sungenis, Not By Bread Alone (2000/2009)]), Catholic apologist Thomas Nash provides some good insights into the injunction not to consume blood in Leviticus and the reaction of the Jews in John 6:
Drink my Blood: Jesus Unveils a New Way
Because of his Bread of Life discourse, John notes that Jesus was a marked man: “After this Jesus went about in Galilee; he would not go about in Judea because the Jews sought to kill him” (Jn 7:1). Why would many of the Jews seek to kill Jesus? Because they perceived that he was, in effect, urging them to reject the Mosaic covenant. His command to eat his body and drink his blood would be, they believed, a violation of Old Covenant law that would cut them off from Israel. They had thought that Jesus had come at long last, as prophesied, to restore Israel to Davidic kingdom status (see Moa 9:11-12; Is 11:1), a status that had not existed since the sixth century B.C. Consequently, Jesus’ words about his Body and Blood had not merely disappointed many Jews; they also effectively served as a declaration of war. Jesus had not come to fulfill the law as he had claimed (see Mt 5:17), many Jews thought, but rather to abolish it and thus Israel as they knew it. A “false prophet” such as this, they thought, was worthy of death (see Deut 13:1-5).
The misunderstanding of many of the ancient Jews is, in part, understandable. Going back to the time of Noah, God had prohibited the consumption of blood (Gen 9:4). In Leviticus 17:10-14, this prohibition is reiterated and more fully explained. No Israelite, nor any foreigner who sojourned with Israel, could consume blood, lest he be cut off. Why? For God had taught them, “the life of the flesh is in the blood; and I have given it for you upon the altar to make atonement for your souls; for it is the blood that makes atonement by reason of the life” (Lev 17:11; see Heb 9:11-12). God designated animal blood to atone for the Israelites’ sins; blood represented the life of the animal, which was given for the sake of man’s life.
Offering the blood of sacrificed animals turned one toward God in repentance; consuming that same blood posed problems. To partake of an animal’s blood meant to seek the “virtues” of that animal, for example, the strength and courage of a bull. Such consumption would lead one to focus on certain animals in an idolatrous manner, as the ancient Egyptians did in serving their animal gods, which represented demons. In idolatrously seeking one’s life from a lower life form instead of God, man would be drawn down to the moral levels of that species, to act like a beast, as it is observed in the occult world.
When he first expounded on the Eucharist, Jesus was well aware of the long-standing biblical prohibitions regarding the consumption of blood. While many misunderstood him as attempting to abrogate these laws, Jesus was actually seeking to fulfill these laws by calling the Jewish people to a higher level of communion with God. The Mosaic legislation of the Old Covenant was not intended by God to last forever. Indeed, the prophet Jeremiah had foretold a “new covenant” that would fulfill the old one God had made with Israel after liberating them from Egypt (Jer 31:31-34; see Ezek 36:24-28). In bidding his apostles to eat his Body and drink his Blood, Jesus signalled that the time had arrived to establish “the new covenant in my blood” (Lk 22:20).
Given the common perception that consuming the Eucharist would cut one off from Israel instead of fulfilling the Old Covenant, Jesus’ invitation to his first disciples required great faith, an invitation that challenged them to move beyond their image of a political messiah and embrace him as the true Messiah. No longer would the blood of animals signify life for man; rather, the Blood of Jesus himself, poured out in the New Covenant, would actually provide life for man (Jn 6:51). What the blood of animals signified, the Blood of Christ provides. Because his Blood provides redemption, Jesus commands us to drink it (Jn 6:51, 54). (Thomas J. Nash, Worthy is the Lamb: The Biblical Roots of the Mass [San Francisco: Ignatius Press, 2004], 139-41, emphasis in original)
