If you want to try a very divisive cocktail, you need to go no further than the classic Negroni. I absolutely love them, but they are not for everyone. Extremely bitter and astringent - you certainly don't gulp this one down. To me, it's the most "adult" of adult alcoholic beverages. You either love or or despise it.
I hate the negroni. Don't understand it, it's way too sweet, way too bitter, but mostly just sickeningly sweet. Like if it was dumped into a glass of soda water or lemon water it would probably be ok.
Absinthe I think is just divisive because licorice/anise flavor is polarizing. I like it in cocktails, like Sambucca too. I love licorice flavors in general though.