Chefs have it easy. Their title conveys a sense of rank and is easily bandied about without someone getting all up in arms about the origin, meaning, and intention. When you call someone a bartender, sure, it conveys the stuff we want, but there's also a missing dimension. Not all bartenders make their own bitters, research antiquated recipes, or use mushroom stock in drinks (not that I recommend it). So some bartenders want to spiff up their title.
The term “mixologist” made its debut in 1856 in Knickerbocker Magazine:
Who ever heard of a man's coming to bed in the dark and calling the barkeeper a mixologist of tipicular fixing unless he had gray eyes, razor handled nose, short hair and a coon-colored vest.
In 1870, it appears with a more serious tone in “Westward by Rail,” according to Richard Hopwood Thorton in his 1912 American Glossary:
The keeper of the White Pine Saloon at Elko Nov informs his patrons that, “The most delicate fancy drinks are compounded by skilful mixologists in a style that captivates the public and makes them happy.”
I like the latter usage — and perhaps the term would be more useful if it didn't draw a red squiggly line under the word in our mental processor. Some think it's a nonsense word, others think it sounds pretentious. There's a sense that it's like saying “hair stylist” instead of “barber,” or “custodial engineer” instead of “janitor.”