Alec Baldwin's character says something very close to this in his Coffee's for Closers rant in Glengarry Glen Ross ("What's my name? Fuck you! That's my name!") Could that be what you're thinking of?
Maybe Chappelle's Show? He says that in the Popular Copy sketch (the Kinkos parody one) posted by world b free at 1:22 AM on February 21, 2012 [1 favorite]
Maybe related to this exchange from Good Will Hunting (1997)? It's in the third person, though.
Sean: My father was an alcoholic. Mean fuckin' drunk. Used to come home hammered, looking to whale on someone. So I had to provoke him, so he wouldn't go after my mother and little brother. Interesting nights were when he wore his rings... Will: He used to just put a belt, a stick, and a wrench on the kitchen table and say, "Choose." Sean: Well, I gotta go with the belt there. Will: I used to go with the wrench. Sean: Why? Will: Cause fuck him, that's why. posted by sparrow89 at 3:29 AM on February 21, 2012 [6 favorites]
Smut Peddlers had a hit back in 1993 called Fuck You.... That's Why. It was pretty popular in the skate / punk circles for a while - - enough that it immediately popped into my head 19 years later. posted by PSB at 5:22 AM on February 21, 2012
Link here: FU moment at about 3:20.
posted by MoonOrb at 1:01 AM on February 21, 2012 [5 favorites]