If there's one thing I can't stand in interpersonal relationships, it's the cold shoulder. If somebody tries to use it on me, I won't stand for it because I honestly don't see the point in it. I think if you're just like "Alright fine, who cares about you then", then that's equally juvenile and it doesn't solve anything.
What I do is basically force them to talk it through with me and sort it out. After all, if I've done something to upset somebody I'd prefer they tell me about it so that I know for future reference. The cold shoulder and the retaliatory cold shoulder are just petty and the lack of communication gets nobody anywhere.
I also think when you get into the mutual cold shoulder routine, there's a certain degree of stubbornness. Each person wants the other to crack first, because for some reason it's "cooler" not to care or to pretend you don't care about the other person, as though this one bad thing they've said or done has made them utterly dispensable to you. Well, what's wrong with caring about somebody and actively trying to heal your relationship with them? Is it somehow weak? Personally, I'd much prefer that than having to deal with all the pretense and pride.
I think if everybody would get over themselves and just talk to one another, it'd be a much less *****y world.