In 1 Peter, the verb hamartano is used once, and is rendered as “for your faults” (2:20). If we are chastized for our own faults, and not for the sake of Christ, then what spiritual benefit is found in that?
In his use of the word for sin, Peter has a strong emphasis on the penal substitution of Christ for sinners. Christ Himself “did no sin” (1 Pet. 2:22), and was therefore not suffering for his own fault. He in His own person bore our sins in His “own body” so that, we, now dead to sins, might live to righteousness (v. 24). This is yet another clear statement of the great exchange — Christ who had no sin took ours, and we, who had no righteousness, took His. Christ suffered “for sins,” the just for the unjust (1 Pet. 3:18). On the foundation of this glorious justification, we may build a strong doctrine of sanctification. Because Christ has died, the one who suffers in the flesh ceases from sin (4:1).
And above all, of course, we are to have fervent charity because charity covers a multitude of sins (4:8).