In this context, the word 'back' doesn't describe a specific body part - it refers to the wearing of clothes in general. We also have the expression 'clothes on/from (one's) back', to refer to any clothes worn on the whole body. For example:
'Never forget who pays for the food on your table and the clothes on your back.'
This use of 'back' is an example of synecdoche - a device whereby one element represents the whole.
Damon,
The points made about not changing a word in an idiom is an important one.
The other thing to keep in mind is that some of our idioms are decades old, or maybe even more than a century old. I think the ¨shirt off one´s back¨ has been around at least several decades, long before the words ¨t shirt¨ or ¨hoodie¨.
Here is an article about the origin of some common idioms. You can see that many of these, that are still common today, are more than a century old. Generally, the idiom is passed down as it is and not altered to make sense to our modern minds. https://www.oxford-royale.co.uk/articles/bizarre-english-idioms-meaning-origins.html
So the rule is, when you learn an idiom, don´t mess around changing it.
You're absolutely right, that idiom doesn't make a lot of sense. :)
"He would give you the shirt off his back" is the idiom, and you define it perfectly. I think whomever coined the phrase long ago was looking for something a little more poetic than "give you the shirt off his torso" or "give you the shirt off his upper body". Those variants make more sense, but "back" is a little more picturesque. "Back" also resonates with the concepts of "backing someone" (supporting) or "putting your back into it" (really working hard), although I'm not actually sure whether there's any connection. Good question.
That's an interesting question, Damon.
As 'shirt off back' is an idiom, it's perceived as a whole not as individual words. So, I wouldn't replace the word 'shirt' by any others to avoid confusion. I guess it can be done in certain situations if you would like to break this idiom and create some humorous effect but usually idioms are used as they are because they are set phrases. I guess this phrase was coined a while ago so T-shirts might not have been popular back then :)
Another similar one off the top of my head is an idiom 'off the cuff' which means spontaneously, without preparation. Even if you are not wearing a shirt, so have no cuffs and are wearing a casual T-shirt and ripped jeans you can use this idiom and it will sound perfectly ok, nobody will be looking for your cuffs :) It's because these idioms are perceived as a whole, they are trite metaphors speaking in linguistic terms. It means native speakers are so used to them that they don't notice individual words that build these idioms.
