I’ve oft wondered, and nobody has ever been able to give me a straight answer that makes sense.
In movies set in the first three decades or so of the twentieth century, many men can be seen wearing garters on the outside of their sleeves, in the middle of the bicep. I’ve always wondered why. Whats the straight dope?
Sometimes, they were a sign of mourning. Whereas, for a woman, formal mourning meant dressing from head to toe in black garb, a man only needed to wear a single black armband.
My dad used to wear arm garters to keep his sleeves out of the way. I had some from the 1970’s that were made for women’s arms. They were just a fad then.
Usually those were much wider than the usual men’s arm garters. And on only one arm, as you pointed out.
My understanding is that off-the-rack shirts were not offered in various sleeve lengths, and the sleeves were on the long side. Thus fellows with average-length or short arms used the garters to get a reasonable fit.
Yes, shirts were sold with long sleeves. It was also common to sew a fold or pleat into the sleeve (in the middle of the biceps) to shorten the sleeve. I have seen quite a few like thet.
As a corollary, this tradition is still maintained to some extent. For example, Australian Rules Footballers commonly play with a black band of tape around one bicep as a sign of respect for a deceased person.
The underlined OP subject on the prior screen had me thinking, “When did men ever wear quarters on their sleeves?!?”. 
Anyway, great question and responses! I learned something!
I still wear them on occasion (and I’m only in my 30s). Mine are spring-like metal around heavy elastic, and they’re worn just below the bicep. I wear them when I’m wearing a shirt that requires cuff-links, because you want the cuff to stay in the same position when you move your shoulders. Having a little spare material in the sleeve above the constriction allows you to gesticulate wildly without your sleeve riding up.
My unverified understanding of this practice was that in the early days of mass produced clothing, shirts (the cheaper ones) were available in only one size. This worked well because because white shirts were almost regarded as underclothing – men normally wore jackets and maybe waistcoats. (In the summer, you wore a dicky and cuffs under your jacket.) The neck size was not a problem since they were collarless and it just had to be large enough to fasten loosely. A stiff collar was worn separately.
To deal with the sleeves being too long, you wore the garters under your jacket. A bartender is just the sort of person you might see displaying his garters. He was not wealthy enough to afford fitted shirts, not a laborer so he wore dressier clothes, and might have to remove his jacket in a crowded, hot bar.
Isn’t the Title “Why did men used to wear garters on their arms?” bad grammar ?
Sould you not just say “Why used men wear garters on their arms?”
Actually, it should be “Why did men use [not used] to wear garters on their arms?” If it were a declarative sentence, one would say “Men used to wear garters…” In making it a question, “used” is separated into “did use.” We don’t say “did used.” That aside, it is normal correct usage, perhaps idiomatic, but not ungrammatical.
Now, that’s ungrammatical. One could perhaps say, “Why used men to wear garters on their arms?”, but it sounds awkward and unnatural. It might work as a poetic license sort of construction, but it’s definitely not the normal word order, and I’ve never heard it said that way.
Well, maybe. To my ear, though, **Tarantula’s ** version sounds just as lumpy as the title. It also brings an image of a Ralph’s Used Men lot on the corner, with a smiling group of slightly shopworn gents, each wearing arm garters and little “Ralph’s” stickers on their back pockets.
Perhaps “Why did men once wear garters on their arms?” would work.
Back to the question at hand, I know a somewhat antiquarian (I wouldn’t say antiquated to his face) partner at my old law firm that always wore one. (He also always wore pocketwatch with on a chain with a fob in his vest, he was that kind of guy.)
The garter was a springy band of gold-colored metal that he wore on his right arm. I believe its function is to keep one’s cuff up on the arm so that it would not drag and smudge ink of the the fountain (or perhaps quill) pen that you were using on the document you were writing.
Needless to say it was a tad obsolete in the 21st Century, when most people use ball-points when they’re not on the computer. Indeed, he did most of his own typing on the computer, which is surprising in an older lawyer, and I can’t recall him using a fountain pen, except perhaps to sign a document.