The controversies over this text abound, very likely because following out the literal meaning is quite often inconvenient. But there are worse things than inconvenience to say about the literal compliance with such a text. We might say, for instance, that under some circumstances, turning the other cheek might elicit violence where otherwise none might have occurred at all.
I too would like to say something bad about turning the other cheek  but I would like to say a bad thing I have not heard anyone say before. Turning the other cheek might be a valuable opportunity lost. This is why.
All of the cited examples continue to be defined by the same dimension as the offense. Example 1 has to do with cheek-slapping;  example 2 with a successful suit at law; example 3 with military levies of labor; example 4 with with ownership and the control that goes with what is owned. These all have to do with more or less of the offensive behavior—slapping, suing, conscripting, borrowing.
But what is there were an opportunity to change the whole exchange into a different category? Could that be considered “turning the other cheek” or possibly as better than turning the other cheek? I have, as Tom Lehrer says in introducing a march he wrote called “Smut,” “a modest example here.”
Remember the Titans
I’m thinking of a transaction in the movie Remember the Titans. This is a subtle and powerful exchange between Julius (Wood Harris), the best black player on a recently integrated football team, and Gerry (Ryan Hurst), the captain of the team and arguably the best white player.
Coach Herman Boone (Denzel Washington) has required the black and white members of the team to get to know each other and he is holding three a day practices until they do. In Pennsylvania. In the summer.
The argument between Julius and Gerry goes back and forth in racial terms. If, at that point, the norm of turning the other cheek had been introduced, no progress would have been made at all. But Julius turns the question so that it raises to Gerry’s official role as team leader. If he is really the team leader, why doesn’t he do something about a major flaw in the team’s performance; why doesn’t he require the white linesmen to block for the black ballcarrier?
The effect Julius gets might have been demanded as a matter of racial justice. That case would go that people like you (white players) are cheating players like me (black players) because of your racial bigotry and you need to stop. That wouldn’t have worked at all and that is not, in fact, what Julius did. Julius took this damnable racist action and put it into another context. The old context was a zero sum struggle: whatever black players gain, white players lose. The new context is in a positive sum, a win/win, context.
The new context does not require Julius to give up his grievance. It is a fact they both recognize that the white linemen are dogging it on the plays where a black man is carrying the ball. What Julius does is to relocate that grievance so that it is part of the job of his superior, the captain of the team. And what Gerry does is to accept the challenge not as a white player but as the captain. As a white player, he had done everything that can be demanded of him, but as captain, he has been complicit in the behavior of his white teammates. He has not called them for their bad football behavior (not blocking) because calling them out on that would be seen as a racial matter—and when he does it, it is seen that way. But as captain, he really doesn’t have a choice.
Imagine that Julius hated all white players and also hated losing. He has to be willing to call one of these white players, “Captain.” That means he is granting a formal rank higher than his. What he gets for that sacrifice is that the losing stops. Julius changed the set of relevant categories from black and white, a zero sum conflict, to leader and follower. In the new category, the leader is obligated to do something he has not been able to do, and acting as a leader rather than a “white player” opens up a positive sum (win/win) strategy of benefit to both Julius and Gerry. 
The options Jesus specifies have in common that the aggrieved person give up his rights. Julius did, in fact, give up his rights as a black man and asserted, instead, his rights as a follower of the captain. He demanded that the captain do, because of his superior rank, what he had been unwilling to do before. Does this require sacrifice and self-discipline? Of course it does. But look at what you get for it.
This doesn’t just end tit for tat within the same category of behavior. This changes the category entirely. I say that’s a good thing.
Bargain for Frances
The second example comes from a children’s book called A Bargain for Frances. Frances is a very well-mannered little badger who is being routinely abused by her playmate, Thelma. No one, looking at this situation, would recommend that she “turn the other cheek.” That is what she is doing already; it is all she has ever done and the results have been really bad.
In this story, Thelma cheats Frances out of a tea set and Frances finds out about it. Following the idea that “turn the other cheek” is a mandate that locks you into the same channel that contained the offense, we could say that Frances could go out and buy another tea set and give that one to Thelma as well. What she could not do, following that mandate, is to deceive Thelma and get her tea set back and that is what she does.
Thelma instantly recognizes that the fundamental relationship she has always enjoyed with Frances has vanished. The old relationship was the relationship of predator (Thelma) to prey (Frances). Clearly that was not good for Frances, but I would argue that it wasn’t really good for Thelma either.
Perceiving the new relationship—as yet unnamed—Thelma says, “I can see that when I play with you, I will have to be careful.” Thelma might have meant that now each can harm the other, so at least a grudging respect, is required. Maybe Thelma meant that now that Frances has claimed the right to personhood on the same grounds as Thelma, they will have to treat each other as competitors, each taking advantage of the other when the occasion arises. Russell Hoban, the author, doesn’t speculate. He leaves that to me.
He does give Frances the last word, however, so we know where his heart is. Frances picks up on the language in Thelma’s remark—“careful,” Thelma said—and says, “Would you rather be careful or would you rather be friends?” Having earned the status of co-predator, Frances offers something better. She offers friendship a relationship that was never an option before and one that turning the other cheek would not have generated.
I am making the argument that there is nothing in the stream of evil and nonresistance that opens the chance of a new relationship at all. This is the end of the zero sum relationship of competitors—what I win, you lose. This is the offer of a positive sum relationship in which both can win and in which, in fact, neither can win without the other.
Does this count as “turning the other cheek?” I think if you read it tightly so that the response is the same kind of thing as the provocation, it does not. Frances does not offer to be cheated again, to buy and give another tea set, to loan her tea set to Thelma and never ask for it again. Those are all the same kind of action as the provocation. But what if you can “turn the other cheek” by transforming the action into another kind of action entirely?
I argue that it is a “turning the other cheek,” understood more broadly. In this way of looking at it, turning the other cheek, as well-motivated as it might be, is transcended by turning the whole relationship on its head.
That seems better to me.
 And the accompanying three: the cloak as well as the tunic, the second mile as well as the first, the obligation to lend.
 I understand this to be an insult rather than a beating.
 They also become lifelong friends, but that is another story entirely.