Jesus knew no sin, yet He became sin for us. We see the idea of someone bearing sin in the place of others attested to in both the OT and NT (cf. Lev. 10:17; 16:21-22; Is. 53:6, 11-12; Jn. 1:29). Jesus is the Lamb without blemish that takes away our sin by dying in our place but He also rises; priest and lamb are not His only office. Jesus is also the coming King who reigns eternally. Consequently, union with Christ as our corporate head not only brings appeasement from wrath but entrance back into the true Promised Land. So, the gospel is the good news of the Kingdom through the cross.
Hughes says of 2 Cor. 5:21 that “there is no sentence more profound in the whole of Scripture.” It is profound, amazing, and unexpected because although Jesus knew no sin He is treated as sin personified. What is further remarkable is that while “Christ alone in actuality suffered the penalty for sin, all are regarded as though they had suffered it themselves.”
So John Calvin asks, “How are we righteous in the sight of God?” And he answers:
It is assuredly in the same respect in which Christ was a sinner. For he assumed in a manner our place, that he might be a criminal in our room, and might be dealt with as a sinner, not for his own offences, but for those of others, inasmuch as he was pure and exempt from every fault, and might endure the punishment that was due to us—not to himself. It is in the same manner, assuredly, that we are now righteous in him—not in respect of our rendering satisfaction to the justice of God by our own works, but because we are judged of in connection with Christ’s righteousness, which we have put on by faith, that it might become ours. On this account I have preferred to retain the particle ἐν, (in) rather than substitute in its place per, (through,) for that signification corresponds better with Paul’s intention.
So, what v. 21 means is that “Christ was made to bear the consequences for our sins.” God has imputed to Christ something that was extrinsic to Him and imputed to us something that was extrinsic to us. This is the great exchange: Christ gets our sin and we get Christ’s righteousness.
The people’s sins are on or in some ways “in” the sacrifice (Lev. 16:5-10, 20-22). The people do not have solidarity with the sacrifice in the same way that they have solidarity with Adam but there is still a clear connection. However, Jesus the Christ has the role of sacrifice and second Adam. So, there is solitary with the Lamb of God that takes away the sin of the world so in Jesus’ death and resurrection all those “in Him” are also said to have died and been raised (cf. Rom. 6). This is a function of the unique office that Jesus Christ has. He is the beginning of the new humanity. Ridderbos says, “Reconciliation constitutes the foundation of the new creation, of the fact that the old has passed away, that the new has come (2 Cor. 5:17, 18).”
 For Καταλλάσσω see Romans. 5:10; 1 Cor. 7:11 for καταλλαγή Romans. 5:11; 11:15 and for ἀποκαταλλάσσω Eph. 2:16; Col. 1:20, 22.
 Charles Hodge says, “To Reconcile is to remove enmity between parties at variance with each other.” (Hodge, Commentary on the Second Epistle to the Corinthians [Grand Rapids: William B. Eerdmans Publishing Co., 1994], 142).
 We see this throughout the NT; see Matt. 27:4, 24; Lk. 23:47; Jn. 8:46; Heb. 4:15; 1 Pet. 1:19; 2:22.
 See Colin G. Kruse, The Second Epistle of Paul to the Corinthians (Grand Rapids: Wm. Bible Eerdmans Publishing Co., 1987), 129-30 for the wrath that Jesus endured.
 Hughes, Paul’s Second Epistle to the Corinthians, 211.
 Although, it is foreshadowed for example in the sacrificial system, Is. 53, and elsewhere.
 “Paul is not saying that at the crucifixion the sinless Christ became in some sense a sinner, yet he is affirming more than that Christ became a sin offering or even a sin bearer. In a sense beyond human comprehension, God treated Christ as ‘sin,’ aligning him so totally with sin and its dire consequences that from God’s viewpoint he became indistinguishable from sin itself” (Harris, The Second Epistle to the Corinthians, 454).
 Thrall, The Second Epistle to the Corinthians, 410.
 Calvin, Commentary on the Epistles of Paul the Apostle to the Corinthians trans. John Pringle (Grand Rapids: BakerBooks, 2003), 242. N. T. Wright sees things differently. He says the righteousness of God “has routinely been understood in terms of the righteous status which the covenant god reckons or ‘imputes to believers, but this interpretation then regularly leaves the verse dangling off the edge of the argument. Every other time Paul uses the phrase dikaiosune theou, he refers, not to the status which believers have from this god (ek theo, as in Philippians 3.9), but to God’s own righteousness, God’s faithfulness to the covenant, the faithfulness through which the new creation is brought to birth.” (N. T. Wright, The Resurrection of the Son of God, 305).
 Kruse, The Second Epistle of Paul to the Corinthians, 129. “The reconciliation which God effected in Christ is the removal of this barrier by his not counting their trespasses against them. The basis upon which this non-reckoning of sins was made possible is indicated in v. 21” (Ibid., 127).
 Harris says, “if ἁμαρτία is parallel to δικαιοσύνη θεοῦ, it is more likely to bear a judicial or forensic sense than a sacrificial or cultic meaning” (Harris, The Second Epistle to the Corinthians, 453). Yet, Harris also says that it seems like Paul had Isaiah 53 in his mind when he penned v. 21 (21a/Is. 53:9, 21a/53:10, 21b/Is. 53:11) (See Harris, The Second Epistle to the Corinthians, 456).
 Ridderbos, Paul, 183.