Some may have taken the Old Testament guideline (see Exodus 21:23-25) in a literal fashion. At first glance, it seems that, if a person's tooth or eye were lost in a scuffle or accident, the one who caused the loss to happen would be required to forfeit his own tooth or eye. Though some may have demanded this in times past, it is clearly not God's intent for the law. Instead, it is a principle, given in concrete, understandable terms, that damage is to be justly compensated.
According to commentator Adam Clarke, the Jews of Christ's day abused this law to extract every last penny from another, and in the majority of cases, there was no mercy shown. Human nature being what it was then, and still is now, they insisted that the one who caused the problem receive every bit of punishment coming to him. In short, they wanted and exacted revenge! Jesus wants us to understand that His disciples are not to act this way.
In countering the faulty understanding of this Old Testament law, Jesus teaches, "But I tell you not to resist an evil person. But whoever slaps you on your right cheek, turn the other to him also" (Matthew 5:39). He begins by instructing us not to escalate the situation by stubborn resistance or, worse still, by perpetrating an additional offense. Elsewhere, Paul writes, "Repay no one evil for evil" (Romans 12:17). If offended, do not offend in return. If injured, do not inflict an injury in payment. In other words, retaliation is not the answer.
Note that Jesus is not speaking of dangerous situations, like facing a robber with murderous intent or a rapist on a dark street. On His mind are circumstances of daily life that are insulting, bothersome, or even mildly injurious, but not life-threatening. The Interpreter's Bible comments on the latter half of the verse: "A blow with the back of the hand to the right cheek was an insult, thus the palm of the hand was now poised to bring a blow to the left cheek." The blow is struck contemptuously rather than homicidally.
In a situation like this, the first thing that comes to most minds is revenge. Jesus desires that, rather than avenging oneself and acting with the same attitude of hatred as the aggressor, we reflect our calling and suppress the urge to seek vengeance. We should even be willing to take a second slap, this one from the other's open hand, without retaliation. Such pacifism usually pours cold water on the situation, avoiding further tit-for-tat retribution.