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Is the "eye for an eye" rule of the OT countered by Matthew 5:39, "Resist not evil; but whosoever shall smite thee on thy right cheek, turn to him the other also"? Is Jesus countering the OT law here?
Historical and literary context say no. In this section of the Beatitudes, Jesus offers points taken from the Pharisaic oral law and refutes them: The sort of wrangling that was done to, for example, get around the "no work on the Sabbath" restriction by nailing a board between two houses so that they could be technically counted as one house.
There was an "extra layer" of meaning added to the OT by the oral law, and in this particular case, the layer was added to suggest that "eye for an eye" was not only for civil matters of justice -- as the OT intends -- but also for interpersonal relationships; hence, the examples that follow of someone being slapped, or being forced to carry a Roman soldier's pack, or being sued: Things that may have been irritating or inconvenient, but were by no means illegal.
To strike someone as described was an insult against their dignity (usually, only slaves were given such treatment), but it was no crime: Even so would the oral law have insisted that it was just fine to use the principle of lex talionis for personal revenge on the one who had humiliated you.
"Resist not evil" is a popular Jewish proverb (cf. Ps. 37:1, 8; Prov. 24:29) which means, in essence, do not compete with evildoers, trying to "outdo" them in vengeance. (As Bivin and Blizzard put it in Understanding the Difficult Words of Jesus, if your neighbor dumps a pail of garbage on your lawn, "we are not to retaliate by dumping two pails on his lawn." )
In other words, don't try to get back at them in more spectacular ways. That is the point of this rebuttal -- it is NOT an abrogation of the OT at all.