Why, he means, am I telling you that you must keep peace? For I even insist upon your doing kindness. For he says, “give him to eat, and give him to drink.” Then as the command he gave was a very difficult and a great one, he proceeds: “for in so doing you shall heap coals of fire upon his head.” And this he said both to humble the one by fear, and to make the other more ready-minded through hope of a recompense. For he that is wronged, when he is feeble, is not so much taken with any goods of his own as with the vengeance upon the person who has pained him.
For there nothing so sweet as to see an enemy chastised. What he is longing for, then, that he gives him first, and when he has let the venom go, then he again gives advice of a higher tone, saying, “Be not overcome of evil.” For he knew that if the enemy were a very brute, he would not continue an enemy when he had been fed. And if the man injured be of ever so little a soul, still when feeding him and giving him to drink, he will not himself even have any farther craving for his punishment.
Hence, out of confidence in the result of the action, he does not simply threaten, but even dwells largely upon the vengeance. For he did not say, “you shall take vengeance” but, “you shall heap coals of fire upon his head.” Then he further declares him victor, by saying, “be not overcome of evil, but overcome evil with good.” And he gives a kind of gentle hint, that one is not to do it with that intention, since cherishing a grudge still would be “being overcome of evil.” But he did not say it at once, as he did not find it advisable yet. But when he had disburdened the man of his anger, then he proceeded to say, “overcome evil with good.”
Since this would be a victory. For the combatant is rather then the conqueror, not when he brings himself under to take the blows, but when he withdraws himself, and makes his antagonist waste his strength upon the air. And in this way he will not be struck himself, and will also exhaust the whole of the other's strength. And this takes place in regard to affronts also. For when you do affronts in return, you have the worse, not as overcome (so 1 manuscript νικηθεὶς, Sav. κινηθεὶς) by a man, but what is far more disgraceful, by the slavish passion of anger.
But if you are silent, then you will conquer, and erect a trophy without a fight, and will have thousands to crown you, and to condemn the slander of falsehood. For he that replies, seems to be speaking in return as if stung. And he that is stung, gives reason to suspect that he is conscious of being guilty of what is said of him. But if you laugh at it, by your laughing you do away with the sentence against you. And if you would have a clear proof of what has been said, ask the enemy himself, when he is most vexed?
When you are heated, and insult him in return? Or when you laugh at him as he insults you? And you will be told the last rather. For he too is not so much pleased with not being insulted in return, as he is vexed because his abuse was not able to gain any hold upon you. Did you never see men in a passion, how they make no great account of their own wounds, but rush on with much violence, and are worse than very wild boars for seeking the hurt of their neighbor, and look to this alone, and are more given to this than to being on their guard against getting harmed?
When therefore you deprive him of that he desires most, you bereave him of everything, by holding him thus cheap, and showing him to be easy to be despised, and a child rather than a man; and you indeed have gained the reputation of a wise man, and him you invest with the character of a noisome beast. This too let us do when we are struck, and when we wish to strike, let us abstain from striking again. But, would you give a mortal blow? “Turn to him the other cheek also”, and you will smite him with countless wounds.
For they that applaud, and wonder at you, are more annoying to him than men to stone him would be; and before them, his conscience will condemn him, and will exact the greatest punishment of him, and so he will go off with a confused look as if he had been treated with the utmost rigor. And if it is the estimation of the multitude that you look for, this too you will have in larger share. And in a general way we have a kind of sympathy with those who are the sufferers; but when we also see that they do not strike (several manuscripts resist, ἀ ντιπίπτοντας) in return, but even give themselves up to it, we not only pity them, but even feel admiration for them.
Source: Homilies on Romans (New Advent)