Medieval and Renaissance theories about the Atonement appear to suffer from a common and easily identified misunderstanding, and I take it to be this: They all assume that there is some need in God that must be met and satisfied by Christ's sacrifice on the Cross. Something in God is the beneficiary of the Cross, whether His honor, or His justice, or His wrath, or whatever. These theories postulate in God some requisite that could only be addressed by the suffering and death of Christ. God—or some aspect of God—is the beneficiary of sacrifice.
I submit that an idea of this sort is very difficult to sustain from biblical teaching about sacrifice. There are simply too many scriptural texts insisting that God does not need it. Introducing a brief survey of such texts, St. Augustine comments, "And who is so foolish as to suppose that the things offered to God are needed by Him for some uses of His own? Divine Scripture in many places destroys such an idea" (The City of God 10.5). Augustine then goes on to cite several texts from the Psalter to this effect, limiting the number "so as not to be tedious."
If God does not need sacrifice, however, man certainly does, because "whatever correct worship is paid to God profits not Him, but man." Man, then, not God, is the beneficiary of a sacrifice offered to God. God does not need sacrifice, but man needs to offer it.
This quotation is a selection from Pastoral Ponderings by Fr. Patrick Reardon. Here is the complete Pondering on the Atonement.