Blood is the thing. In the Scriptures, sin must be covered or "atoned for" as it's called, by blood. You see, God hates sin. But God also wants to enjoy a faithful, loving, and kind relation with his people whom he loves. The trouble is, his people prefer to turn to things that are not God rather than God. The way God deals with this is simple: God provides a blood sacrifice for their sin, and they carry out the ritual.
God's people don't go to him with their blood sacrifice, the Lord comes to them with his blood sacrifice. Over and over again in the Bible we see this play out. People chase after their own gods, turn their backs to true the Lord, and he's got to rescue them from the power of sin. God does this because he's a God of grace and mercy. The way God moves from judgment of sin to grace and mercy is blood. Blood sacrifice is the primary thing that erases judgment to make an atonement for the sin of his people, and restore the right relation between the Lord and his people.
Leviticus, for example, is a pretty bloody book. Sacrifices and offerings are a bloody business, it turns out. Blood on the altars. Blood on the holy instruments. Blood on the floor. Blood on the people. You get the idea. In Leviticus, you can't get away from the fact that Israel's worship isn't what we'd call "seeker sensitive." The picture of sin and it's forgiveness isn't pretty. It's painted with actual blood.
But why so much blood? Because "the wages of sin is death," and "the soul that sins will surely die." On the other hand, there's life in the blood. That's why, if you don't want to die for your sin you've got to find someone or something to give it's life for you. You must provide a substitute. When its blood is poured out, life is poured out. Its life for your life. It's blood to cover your sin. "For the life of the flesh is in the blood, and I have given it to you on the altar to make atonement for your souls, because it is the blood by reason of the life that makes atonement" (Leviticus 17:11).
That's how it happened. An animal's life for the life of a person. God's judgment against sin was transferred from the sinner to the animal sacrifice. The Passover Lamb or scapegoat was a substitute for the one offering it. When the animal's blood was poured out that person's death was considered to have happened. As a consequence, the Angel of Death passed over him.
And as the Letter to the Hebrews says, "according to the Law, one may almost say, all things are cleansed with blood, and without shedding of blood there is no forgiveness." That's why Jesus had to do what he did.
You see, the whole Old Testament system of blood sacrifice was pointing to Jesus' sacrifice. That's why, when John the Baptizer saw Jesus, he said, "Behold, the Lamb of God, who takes away the sin of the world!' John believed Jesus was the blood sacrifice for the sin of the world, not just Israel. By Jesus' shed blood all people would have their sin covered one time, for all time.
The apostle Paul also writes that, "In [Jesus] we have redemption through his blood, the forgiveness of our trespasses, according to the riches of his grace, which he poured out upon us" (Ephesians 1:7-8).
Until Jesus came, God passed over sin because of the blood of sheep and goats, and other animals. When Jesus died on the cross, God didn't pass over sin anymore. He took sin away. God's demand that sin be atoned for was satisfied whole and complete by Jesus' blood.
This is why Jesus' words in John's Gospel and at the Last Supper are so important in the present tense. He says that unless we "eat his flesh and drink his blood there's no life in you." Also, he says, "drink it, all of you; this cup is the New Testament in my blood, which is shed for you for the forgiveness of sin..."
Jesus' words point us backwards to the Old Testament sacrificial system, that it's all about him. He also points us to the present tense, that he is the end of blood sacrifices. Jesus teaches us that wherever his body and blood are received, eaten, and drunk all those who participate in it receive his actual body and blood, because without blood there can be no atoning for sin.
There can be no certainty or comfort for the believer that his sin is covered, erased, and forgotten in the present tense unless the blood of the Lamb of God is there.
The blood of bulls and goats were not able to take away our sin once and for all. They only pointed Isreal to what was to come. A complete blood sacrifice for all people. Jesus is that blood sacrifice. He "entered the heavenly sanctuary with his own blood to make atonement for us. By his dying he broke the veil of his flesh and sprinkled his own blood upon the mercy seatin the heavenly tabernacle in the presence of God. Christ put away sin by the sacrifice of himself" (Hebrews 9:25f).
The Old Testament roots of the Lord's Supper lay out for us why Jesus' blood is the thing. The blood of animals could never permanently cover sin. The blood of animal sacrifices can be sprinkled on a person's skin, but it can't change their heart or put their conscience at ease, that they're in a good relation with God. But the blood of Jesus, when it's received and drunken in faith, not only cleanses from sin but gives each Christian a peaceful heart and joyful conscience because he knows for certain that God is pleased with him for Christ's sake.