Scripture, on the other hand, affirms that it is Jesus Christ Himself who atones for sin. Atonement for sin does not involve our suffering in addition to what He has done on our behalf. Christ's work on the cross has ensured that we obtain redemption and the forgiveness of sin. It was done "by His own blood" (Hebrews 9:12).
Scripture does not bring together our pain and suffering with the shed blood of Christ in the manner of making atonement. It only speaks of His blood and His suffering for our sins (Hebrews 9:26-28; 13:12; 1 John 1:7; Revelation 5:9). He alone took that burden from us. Any other atoning work is rendered unnecessary. There is nothing we can offer that has redemptive significant for ourselves, let alone other people. Psalm 49:7 tells us that, "No one can redeem the life of another or give to God a ransom for them."
Roman Catholic apologists sometimes appeal to texts such as 2 Corinthians 1:5-7, Colossians 1:24, and Galatians 2:20 in order to substantiate the idea that our suffering can cancel out punishment for sins committed by ourselves and for other people when offered together with the sacrifice of Christ. These verses have been taken out of context, however.
Regarding the text from 2 Corinthians, hardship for preaching the gospel resulted in it being shared and exemplified to the Christians dwelling at Corinth. Suffering can produce comfort and hope in God which can be shared with other people.
Regarding the text from Colossians, one commentator explains, "That which is behind of the sufferings of Christ — That which remains to be suffered by his members. These are termed the sufferings of Christ, 1. Because the suffering of any member is the suffering of the whole; and of the head especially, which supplies strength, spirits, sense, and motion to all 2. Because they are for his sake, for the testimony of his truth. And these also are necessary for the church; not to reconcile it to God, or satisfy for sin, (for that Christ did perfectly,) but for example to others, perfecting of the saints, and increasing their reward."