Something that I have noticed while trying to write about this experience is that there is a cultural conversational shorthand in my area of the world in which “drinking” tends to mean “drinking alcohol”. It has made me curious as to why this is, but also at a loss as to how to look up this very precise etymological quirk.
Instead, I am going to make some wildly unfounded hypothesises, but would very much like to know if any of them are at all close, so if you have a lead on this subject, please do let me know.
“Would you like to get a drink with me?” is an adult asking another adult on a date, and our culture associates dating with drinking, as part of the “getting to know you” phase.
“A Drink” is short hand because any other fluid intake is usually explained in context.
-I think I need some water.
-I need my morning coffee to function.
-Tea is an import part of curling up with a book.
“A Drink” is short for “Alcoholic Drink,” whereas “I would like a drink of water” explains the exact liquid required.
After watching characters on Grey’s Anatomy having horrid days, we always know that one character asking the other, “hey, wanna go for a drink?” means that they are going to Joe’s for alcohol (although it will vary between scotch, tequila, and beer depending on the character and the day).
Saying “A Drink” is easier than specifying something for which the other person might not be in the mood, or means you haven’t decided what beverage you want. This does not explain on it’s own why “a drink” seems to mean “an alcoholic drink,” but mixed with the above hypothesises, it could be a factor.
Side note: there is a similar cultural phenomena of asking someone to go for coffee, but this does not bind them to having to drink a coffee-based beverage. This seems to be the alcohol-free version of this shorthand. (Or, in the case of Luke Cage, it is code for sex. Being demisexual, I would not pick up on that cue and things would get really awkward really quickly.)
If you have any random (or factually-backed) hypothesises, please let me know, as I am fascinated by this turn of phrase.