What’s a cocktail?

According to the Online Etymology Dictionary, the word cocktail first surfaced
around the turn of the 19th century. No one knows for sure where it came from,
although H.L. Mencken, the eminent Baltimore journalist and essayist, lists no fewer
than seven possible points of linguistic origin, including a drink stirred with the tail
feather of a rooster.
Another legend has it that a barmaid in New York State used a rooster’s tail to stir
the hot toddies she provided to male visitors because folktales based on the virility
of roosters had it that the cock’s tail had aphrodisiac qualities.
Perhaps the most likely antecedent is the French word coquetier (eggcup). This
proposal is bolstered by the fact that New Orleans apothecary Antoine Amédée
Peychaud (the man who created the still-famous Peychaud bitters in mid-
18th-century New Orleans) is reported to have held social gatherings in his
drugstore, where he mixed brandy with bitters and served the drink in, yes, an
eggcup. In other words, the coquetier, which in English sounded like cocktay and
slid seamlessly into cocktail.
You pays your money and you takes your choice.