A modern may best understood the "turning of the cheek" by reference to the morality of the ancients:
In Sophocles’ Ajax, after the burial of Achilles, both Ajax and Odysseus lay claim to his Hephaestus-forged armour and a contest of rhetoric is held to determine the strength of their respective claims. Odysseus proves more eloquent and Agamemnon and Menelaus bestow Achilles’ armour upon him. The rhetorical contest here intervenes as the potential conflict becomes apparent; the decision of ownership is left to the sacred intermediaries of divinity, the Achaean kings.
Furious at his loss, Ajax slaughters the sheep of the Greeks; for deceived by Athena, he takes them for Odysseus, Agamemnon and Menelaus. Although sheep are traditional sacrifices for the Greeks, as their massacre occurs outside the structure of ritual, and as the malignancy of Athenian madness dissipates, Ajax recognises his disgrace in the spilling of sacrificial blood, and responds by committing suicide. The suicide of Ajax is thus a resolution to the potential for violence against his family; Teucer protects Eurysaces, the son of Ajax, and Odysseus argues for the burial of Ajax according to the same principle.
The turning of the cheek aims, by a higher logic, at the final resolution of minor conflicts before they spiral out of control, not by responding in turn with violence, but by the conversion of all to the Catholic religion.
As Christ says: "Love your enemies, do good to them that hate you. Bless them that curse you, and pray for them that calumniate you” (Lk. 6:27-28); and as it is written: [we are taught] "not to render evil for evil…but to overcome evil by good" (Rom. 12:17,21).
But to love those who hate, curse or calumniate us does not give them a right to hate, curse or calumniate us, nor a right to immunity for hating, cursing or calumniating us. For hate, evil and calumnies are evil, and evil has no right, nor even a right to immunity.
St. Augustine pleads in a letter to Macedonius, the imperial vicar of Africa, that the death penalty be not applied to heretics, hoping that this clemency would help them to convert - the primary desire of the Church. He writes: "Spare the wicked, thou good man; the better you are, the meeker you ought to be; the higher you are by your power, the more humble you ought to be by piety!"
Yet St. Augustine writes a little further: "Now it is true, as morals go in our days, that men want both to be exempt from penalty for their crimes, and yet to possess that for which they admitted the crime [i.e., to continue in their sins]. These are the worst kind of men…"