Only in Matthew's gospel does Jesus say...This is the blood of the new covenant shed for you and for many FOR THE FORGIVENESS OF SINS...what exactly do you think/believe that Jesus meant by that?
Things are a bit more complicated textually than the questioner assumes. First, the passage in Matthew (26:28) exhibits some textual variation among Greek manuscripts. Although the great mass of later manuscripts have "my blood of the new covenant which is shed for many for remission of sins," the earliest witnesses (and those generally regarded as better preserving the "original" readings) have "my blood of the covenant which is shed for many for remission of sins". The Gospel of Mark (14:24) likewise has as the likely more original reading "my blood of the covenant which is shed for many". Luke (22:20) has "this cup is the new covenant in my blood which is shed for you" (as the best-attested reading).
These various references to "covenant" and "new covenant" allude to Old Testament themes. A "covenant" (or treaty/agreement) typically involved blood-sacrifice as part of the ritual. In the OT the people of Israel are pictured as related to God via a covenant, which is described as sealed with a ritual involving the blood of a sacrificial animal (Exodus 24). So, the Gospels scenes picture Jesus as referring to his "blood" (referential to his looming death) as establishing a "covenant" likewise. Luke's reference to the "new covenant" alludes to Jeremiah 31:31-34, where God promises a "new covenant" that will involve salvation for his people.
The larger point is that the Gospels present Jesus' death as made the basis for a new relationship with God, a new "covenant"-relationship that involves God's salvation, and a corresponding human responsibility to accept this new relationship and live in its light.
You are right that only in Matthew does Jesus speak about "forgiveness of sins" at the Last Supper. Matthew has probably adapted Mark, in which Jesus says, "This is my blood of the covenant, which is poured out for many" (14:24). Matthew repeats that sentence and adds "for the forgiveness of sins" (26:28). Matthew, however, probably did not originally say "new" covenant, but a copyist has inserted the word "new" based on Luke's and Paul's version of the "words of institution," as they are sometimes called (Luke 22:25; 1 Cor 11:25). The words "new covenant" come from Jeremiah 31:31-34, where God promises to make "a new covenant" with Israel and Judah, which will be written on their hearts. Jeremiah links the new covenant with forgiveness of sins (31:34). See also Jeremiah 32.36-41 and the "everlasting covenant," as well as Ezekiel 34:25-31 and the "covenant of peace" and Ezekiel 36:26-28 and the "new heart" (which is special to me because of my last name Newheart). Luke and Paul make explicit what is implicit in Matthew and Mark: Jesus' death inaugurates this "new covenant" promised by Jeremiah.
The phrase "the blood of the covenant" comes from Exodus 24:1-8, where oxen are sacrificed as "offerings of well-being." Moses reads "the book of the covenant," which he has just received from God, the people agree to do it, and then Moses dashes the ox blood on the people as "the blood of the covenant that the Lord has made with you" (24:8). When Jesus speaks of the "blood of the covenant," he links his death with what God did at Sinai for this group of recently released slaves.
In Matthew Jesus says that his blood is "poured out for many, for the forgiveness of sins" (26:28). Jesus is here connecting covenant and forgiveness, as in Jeremiah 31. Jesus has previously said that he "give[s] his life as a ransom for many" (Matt 20:28). ("Many" is an idiom for "all." See Isa. 53:6, 12.) Jesus does not discuss how his death is a ransom or how it results in forgiveness. I respectfully disagree with Mr. Mott's comment above that Jesus says that he is "taking on the punishment for sins" and faith in him is required for forgiveness. I simply do not see such a perspective in Matthew. Faith for Jesus is faith in God and in God's forgiving, wonder-working power in Jesus. (See Matt 8:10; 9:2 etc. Things, however, change in the Gospel of John, where Jesus speaks constantly of faith in Jesus. See 3:16; 14:1 etc.) Forgiveness, healing, and power are all part of Jesus' message about the kingdom of God (or kingdom of heaven, as Matthew often has it). This message resonates throughout the Old Testament. As the prophet-like-Moses, Jesus faces his violent death and integrates all these elements in his words at table. May we eat at this banqueting table and then go, convinced that we are forgiven, empowered and healed, to face a violent world!
"for the forgiveness of sins" is Matthew's emphasis on "Jesus' death for many" rather than Matthew only argues for it. For example, Paul discusses that expression in his letter Romans with all of his effort and energy, which Luke and Hebrews accepts. Mark presupposes it as well.
So in my opinion, that belongs to the common stock theology of the earliest churches.
-- Simon Lee
In Paul's I Corinthians 11:25, and then in all three Synoptic Gospels, Jesus says "This is my blood of the [new] covenant..." or words to that effect. Only Matthew adds "for the forgiveness of sins." Now Jesus' death on the cross was interpreted most likely by Jesus, and then by just about all early Christians, as being "for the forgiveness of sins." But on the cross, Jesus' blood was indeed shed. So when, at the Last Supper, Jesus poured out the wine as a symbol of his blood about to be "poured out" at the crucifixion, it was only appropriate to interpret that outpouring of the wine as being "for the forgiveness of sins."
Jesus meant that his upcoming death, represented by "blood," was taking upon himself the punishment for sin so that by faith in himand his death for us, we would receive forgiveness from God.