In my opinion, this is quite different from 'turning the other cheek'. Literally, this is turning your back on whatever it is that's going on ... ignoring it, hoping it will go away or -- at the very least, not still be present when you next look around (or perhaps hoping that it 'never existed' in the first place?).
At one point in my life -- and quite recently, actually -- I was very close to a person who chose to 'walk away' almost every time a conversation (actually, it was most often an argument or a debate) presented itself wherein the 'close person' sometimes found himself at odds with whatever it was that was being discussed/argued/debated.
I asked him why he chose to 'walk away'. His answers differed, depending on the circumstances of his 'walkawayedness'. Mostly, he walked away because:
1. He had no real interest in the topic.
2. He was 'fed up' with the topic.
3. The topic was much too personal. ("Let's talk about the weather!")
4. He was tired, and only dropped by to say, "Hello!", with no further interest in any conversation/argument/debate/whatEVer!
Let's extrapolate on a couple of these answers. Number 1, I think, is self-explanatory. Number 4, as well ... just a simple "Howdy!" might have sufficed.
However, let's take a closer look at #2. WHY was he 'fed up' with the topic? Were there personal issues involved? Or, did not he and his cohorts spend multitudinous hours just the day before (and the day before that, and the day before that, etc., etc.) discussing/debating at great length that very same topic?
If there were personal issues involved, then it's none of your or my business, would you agree? THAT answer exhausted, let's move on to #3 ... "too personal". Well, that's the end of this discussion, isn't it?!?
Until next time, I remain, "Most sincerely/cordially yours .. .." Goldenrod