What you might say when the problem doesn’t concern you, and you may possibly even have a contemptuous lack of interest in the outcome. Some variations are ‘no skin off my tail/behind/back/ass/teeth/ear.’
There are several different theories about the source of this expression. Gregory Titelman’s America’s Popular Proverbs and Sayings claims the expression is of boxing origin and dates from the early 20th century. Perhaps this is because a boxer’s nose is the body part most prone to damage. However, it was not included in the very long list of boxing expressions that I found recently. The expression was used in a 1910 edition of Cosmopolitan.
But others disagree, with some claiming it that its roots are not in the boxing arena but in the mill — that it is, in essence, the opposite of “putting your nose to the grindstone.” The fact that there is no skin off my nose indicates that I didn’t put in as much effort as the person who put their nose in the grindstone, so to speak. But I think that explanation is reaching too far.
Or it may derive from the admonition to keep one’s nose out of another’s business. Again, that’s trying too hard.
“No skin off my back” is the most common version in America, and that apparently comes from the old punishment of flogging. On ships in the eighteenth and nineteenth centuries, flogging was brutal. The condemned would endure a fixed number of lashes with a whip, often made of wet leather straps fastened to a handle. Just a few strokes were sufficient to remove skin from a person’s back and leave permanent scars.
Here’s the most interesting theory. The phrase is said to be a corruption of an old theater expression which was used as a good luck wish. The expression was actually “skin off your nose,” often used as a toast. To people not versed in the ways of the acting profession, losing skin from your nose sounded negative, so in common usage the phrase became mistakenly reversed as “no skin off your/my nose.” This reversal also led to the meaning being slightly shifted. In other words, the actor’s “good fortune” became the layman’s “no harm.”
But why would an actor want to lose skin from his/her nose? Early greasepaints were so gritty that their removal at the end of a performance would scratch the skin and quite literally, on the nose especially, remove some of it. So to have skin off your nose meant to be using greasepaints, which, for an actor, meant to be in work — always good fortune.
I’ve sometimes heard the phrase, in its current meaning, expressed as “it makes no never mind to me.” Which I quite like, even if it isn’t proper English.