It is a response to being wronged. (Note that being sued and forced labour are the parallel cases in Matt 5:40,41 - it's not just about non-violence, it's about our posture towards any and every kind of assault).
When you are wronged the natural response is either retaliation or retreat. You either strike back or shrink away. Jesus commands an entirely different response - standing firm in meekness. Offering the other cheek effectively says:
It hasn't worked has it? You want me to diminish myself - either to run or to descend to your level. But here I am in an apparent weakness that hides unnatural strength. You have not won. I have taken the blow and remain unaffected. I have arrested the cycle of violence and now I stand here confronting you with your own wickedness. I'm outmaneuvering you. I have entirely changed the terms on which we are relating. You may change them back again, but each time I will disempower you by refusing to perpetuate your aggression. I may look like I'm losing. But in reality you lost the minute you struck me. And I refuse to join you. My way - the way of voluntary weakness - is really the only way to win.
Now we know how this tactic has worked en masse. Think of Gandhi's non-violent protest.
But here I want to think about it's transformational power in personal relationships.
Imagine three families where one of the members acts as a kind of scapegoat. The scapegoat is the member of the pack who becomes the perpetual butt of every gag. The family only properly functions when the scapegoat is to blame.
In family A the scapegoat eventually hardens into a sharp-tongued, spikey wise-guy.
In family B the scapegoat shrinks into a self-blaming, shy, clutz.
But what about a third way? Imagine if the scapegoat finds Christ. And in Him finds a power to receive the very worst blow and neither to lash out nor to shrink down.
And so this time the barbed comment comes their way....
Father: You just crashed the car, you stupid clutz! You're always doing that. What's the matter with you, how can you be such an idiot?!
Now scapegoat A would fight back. Scapegoat B would crumble into tears. But in family C the scapegoat says...
Oh Dad, I'm much worse than a clutz. My life is chaotic, I'm always running late, I never look where I'm going. There are some deep seated problems that I'm praying through right now, and 'stupid' doesn't even touch the depths of my problems. But Dad, let's forget about the car for a second and let's talk about why your first response to my car accident was to abuse me? Seems like there's something pretty wrong in our relationship if that's the case...
Wouldn't that be a powerful? Wouldn't that be turning the other cheek?
Or a marriage (could be any marriage!) where the husband comes home late after some ministry activity:
[Fuming] You said you'd be home half an hour ago!
Honey, it was for the gospel! And if you were for the gospel you'd understand!
I give in. I can't win. I'm off to blog...
You're right. There were some unavoidable delays, but at heart you're right - and it's worse than you think. I have this horrible need for people to think I'm a funny, personable guy so I stick around to crack jokes. I put my image ahead of my word to you and that's awful, I'm going to pray about it. But first can we talk about a better way of communicating in these situations?
You refuse to retaliate, you take the blow in all its fullness and then you turn to address the relationship (not the fight).
Now you have a go. Is there a situation where you need to turn the other cheek? How will you do it?
PS - for a brilliant example of Bob Kauflin turning the other cheek to a guy stealing his car battery, listen to the first 5 minutes of this.