Why do we say "It's no skin off my nose"?

Meaning:

It doesn't bother me

Background:

There are a number of different theories regarding the source of this expression. Gregory Titelman's America's Popular Proverbs and Sayings says the expression has its origins in the early 20th century world of boxing. The earliest recorded use is found in a 1910 edition of Cosmopolitan, back when it was called The Cosmopolitan and was a "family magazine" very different from its current incarnation.

But others disagree, with some claiming 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 to the grindstone.

The boxing background appears to carry the most credibility. Incidentally, apparently some say "it's no skin off my teeth", which appears to be a muddled version of "no skin off my nose" and "by the skin of my teeth;" the latter has its origins in the Book of Job: "My bone cleaveth to my skin and to my flesh, and I am escaped with the skin of my teeth."

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