Why: Sometimes the only thing that will help a hangover is a Bloody. Or a beer. Or some club soda with a little bitters in it, and maybe some whiskey. I know the term comes from "hair of the dog that bit you" - so, maybe like, a little hair / shot of Jack is analogous to larger biting dog / the entire bottle one might have indiscriminately poured down one's gullet the night before? No? Anyway, who said it first?
Answer: First: It's more than just an analogy. Instead, it comes from a literal medieval remedy for rabies, as advised in A Treatise on Canine Madness from 1760:
The hair of the dog that gave the wound is advised as an application to the part injured.That sounds even less helpful than a single bloody at Sunday brunch. But it kinda made sense at the time. After all, snake venom was used in the antidote to a snakebite, and the reason I have the flu right now is probably because I got a flu shot...
Secondly: The term's first recorded use in reference to drinking is from 1546. In his A dialogue conteinyng the nomber in effect of all the prouerbes in the Englishe tongue, John Heywood wrote:
I pray thee let me and my fellow haveAnother reference appears in a 1611 dictionary - and in 1661, Samuel Pepys wrote in his diary that found the same method quite helpful:
A hair of the dog that bit us last night -
And bitten were we both to the brain aright
We saw each other drunk in the good ale glass.
Up among my workmen, my head akeing all day from last night’s debauch. To the office all the morning, and at noon dined with Sir W. Batten and Pen, who would needs have me drink two drafts of sack to-day to cure me of last night’s disease, which I thought strange but I think find it true.I want to know what "sack" is.
Source: The Phrase Finder, World Wide Words
The More You Know: On Wiktionary, I see a "rare, humorous" related term - pelt of the dog - that is described like so:
An immoderate, excessive quantity of alcohol drunk the morning after whilst suffering withdrawal symptoms or a hangover, which goes beyond alleviating the complaint to causing drunkennessHo ho!
Right, y'all? Memes.