This is an answer of mine from the Catholic Answers Forum.
What is the initial reason why we would want to consume the blood and body of our beloved Christ?
Hmm... what is the initial reason? I would say because the Lord Himself commanded it. (cf. John 6:29-58; Matt 26:26-28; Mark 14:22-24; Luke 22:19-20; 1 Cor 11:23-25)
Why did He command it? Or, more deeply, why was it under the signs of bread and wine that Jesus commanded us to receive His Body and Blood? Why would He have us consume His Body and Blood? Well, God knows... but He had been preparing Israel for it for centuries.
Melchizedek, king of Salem and priest of the Most High God (long before Israel existed and had priests), offered God a thanksgiving offering of bread and wine, and he blessed Abram. (cf. Gen 14:18-20) And the letter to the Hebrews tells us that Melchizedek was a foreshadowing of Christ. (cf. Heb 7) Melchizedek's name means "king of righteousness", and Salem (shalom) means "peace".
God later tested Abraham, asking him to offer his only beloved son as a holocaust on a mountain. As they went up the mountain -- Isaac carrying the wood for his own sacrificial death on his back -- he asked his father where the lamb for the sacrifice was, and Abraham replied that God would provide Himself the lamb. God did provide an animal for sacrifice in place of Isaac... but it was a ram, with its head caught in a thicket of thorns. (cf. Gen 22)
When God delivered Israel from captivity in Egypt, He instituted a ritual sacrificial meal for them, by which each family was to acquire a spotless, unblemished lamb, to kill it without breaking its bones and to spread its blood upon the doorposts of their homes; the angel of God's wrath, seeing the blood, would pass over them. The family was also to eat the flesh of the lamb. But this was not God's lamb... (cf. Exo 12-13)
In time, another ritual was instituted for Israel, the Yom Kippur ("day of atonement") ritual. Two lambs or goats were chosen, one to be slaughtered in sacrifice, and the other to have the sins of all of Israel placed upon its head and to be sent out into the wilderness to die. This was the "scapegoat", the one who receives the blame and punishment for the sins of others. (cf. Lev 16)
On the shores of the Jordan, John the Baptist called out to all who would hear him, "Behold, the Lamb of God, who takes away the sin of the world!" (John 1:29) He was speaking of Jesus, the only beloved Son of God. (cf. Matt 3:17) Pilate found Jesus to be without fault or blemish. (cf. John 18:38) At His crucifixion, our Lord was crowned with thorns and carried the wood for his own sacrificial death on his back. (cf. John 19:2, 17) His bones were not broken. (cf. John 19:31-36)
St. Paul says that "Christ, our paschal lamb, has been sacrificed." (1 Cor 5:7) ["Paschal" means "Passover"]
St. Paul asks, "The cup of blessing which we bless, is it not a participation in the blood of Christ? The bread which we break, is it not a participation in the body of Christ?" (1 Cor 10:16)
St. Peter says that we "were ransomed from the futile ways inherited from your fathers, not with perishable things such as silver or gold, but with the precious blood of Christ, like that of a lamb without blemish or spot." (1 Pet 1:18-19)
St. John saw in Heaven "a Lamb standing, as though it had been slain." (Rev 5:6)
The angels in Heaven say "Blessed are those who are invited to the marriage supper of the Lamb." (Rev 19:9)
(And why do we drink His blood? Israel was forbidden to consume blood, since the life is in the blood. (cf. Gen 9:4; Lev 17:10-14) That was to prepare them for the only blood they should consume, the Blood of Him Who has eternal life.)