From The Gospel of Matthew by Curtis Mitch and Edward Sri, reflecting on Matthew 26:26-28:
The words of Jesus at the Last Supper inform not only our sacramental understanding of the Eucharist but also our theological understanding of the Messiah’s death. Were one to read Matthew’s Passion Narrative apart from this account, the death of Jesus would seem to be little more than an execution at the hands of Roman authorities. One could reason that Jesus died for an important cause, but the historical circumstances speak of a capital sentence carried out against a perceived troublemaker. Christianity, however, claims that Jesus’ death was a cultic act of sacrifice. It is principally the Eucharistic words of Jesus that give us this insight into the mystery of Good Friday.
First, the blood of Jesus is poured forth as an expiatory sacrifice that effects the remission of sins (see Jer 31:31–34). Second, Jesus offers his life to the Father as a vicarious sacrifice; his suffering is not for his own guilt, but for those he represents and has come to save (see Isa 53:4–5, 11–12). And third, Jesus’ death is a covenant sacrifice that establishes a new foundation on which the Father and the human family can be reunited in fellowship and love (see Exod 24:4–8). According to Matthew, the sacrificial interpretation of Jesus’ death, so prevalent in the New Testament, originates with Jesus himself.