Duck on a first date?
I can only think of four valid reasons that you would serve duck on a first date:
1) You are a gourmand and want to show off your signature canard dish,
2) You are a hunter and you shot the duck yourself,
3) You are aware in advance that duck is your date's favorite dish, or
4) You are a pretentious douche who is trying way too hard.
Sure, there are probably rural areas or culturally diverse areas where duck is a more common food (similar to rabbit), but not in LA.