My question is within the context of Atonement theology. What do you know about 2 Cor. 5.21 "He made Him who knew no sin to be sin on our behalf, so that we might become the righteousness of God in Him."? What does "to be sin on our behalf" mean? I've done some digging, but I will save my thoughts - because I want your response to be a part of everything swirling around in my head.
In a sense, our Lord is our Passover, as Paul says in 1 Cor. 5:6-8 (ESV) Your boasting is not good. Do you not know that a little leaven leavens the whole lump?  Cleanse out the old leaven that you may be a new lump, as you really are unleavened. For Christ, our Passover lamb, has been sacrificed.  Let us therefore celebrate the festival, not with the old leaven, the leaven of malice and evil, but with the unleavened bread of sincerity and truth.
In sync with the Passover event recorded in Exodus, Christ as an innocent Lamb sacrificed his blood as an atonement for our sins, and as our life we feed on him for strength for our journey. If you recall, the sacrificed lamb was the only means by which the people of God could escape the angel of death's slaying of the firstborn in Egypt, whether Hebrew or Egyptian. In the same way, on the Day of Atonement, the High Priest entered into the Holy of holies to sprinkle the blood of the covenant on the ark as an atonement for the sins of the people. The entire book of Hebrews details the way in which both the priesthood and sacrifice of Jesus Christ is superior to that of the Temple sacrificial system, the Levitical priesthood, the Aaronic High Priestly office, and the animal sacrifice. Actually, the author of Hebrews says that these practices and offices where emblems, tokens, signs of the a truer, more definitive and effective heavenly pattern, with our Lord Jesus being both Victum and Victor as High Priest and Offering combined.
This 2 Corinthians 5 text affirms this clear sense in how Jesus became sin for us. Perhaps the clearest understanding of this is seen in the great chapter of the Suffering Servant, Isaiah 53:
Isaiah 53:4-6 (ESV) Surely he has borne our griefs and carried our sorrows; yet we esteemed him stricken, smitten by God, and afflicted.  But he was wounded for our transgressions; he was crushed for our iniquities; upon him was the chastisement that brought us peace, and with his stripes we are healed.  All we like sheep have gone astray; we have turned every one to his own way; and the Lord has laid on him the iniquity of us all.
Notice the end of this matchless text: ". . . and the Lord has laid on him the iniquity of us all," in my mind the Hebrew Bible equivalent to Paul's high Christology in 2 Cor. 5. In his body on the tree, Christ became sin for us, and through faith, we now in the "Great Exchange of Guilt and Righteousness" become the righteousness of God in him. This is the heart of the Anselmic satisfaction theory of the atonement which has reigned supreme in Protestant circles since the Reformation, and it is a sound, biblical, and moving interpretation. I would simply extend its richness to include the Savior's complete victory over the devil, the curse, hell and death, and the principalities and powers through his incarnation, death, resurrection, and ascension. (The Christus Victor motif allows us to give weight also to Christ's matchless life, as well as to his death, and affirm the life-giving power of his resurrection and his exaltation at the Father's right hand through the ascension).
Jesus of Nazareth was both High Priest and Sacrifice, Mediator and Offering, Messiah and Lamb. I think Paul highlights the meaning of his great exchange on the Cross for us, and highlights the merits of his life as they accrue to us. Here is another place and way he says it: Philip. 3:8-10 (ESV) Indeed, I count everything as loss because of the surpassing worth of knowing Christ Jesus my Lord. For his sake I have suffered the loss of all things and count them as rubbish, in order that I may gain Christ  and be found in him, not having a righteousness of my own that comes from the law, but that which comes through faith in Christ, the righteousness from God that depends on faith—  that I may know him and the power of his resurrection, and may share his sufferings, becoming like him in his death.
I hope this is helpful. The richness of Christ's work is extraordinary, both in regards to sin, to righteousness, to death, and to eternal life. What a mighty God we serve!