So, why a dog and not a cur? It is true that many sources say a "ram" finished the race before the monkey, but nowadays, we don't seem offended by Year of the Sheep, instead of Ram. So, why not "Year of the Chicken?" It's not like we're emasculating the Rooster and calling it "Year of the Hen."
Chickens, I guess, have had image problems. There is a dimsum dish which is essentially chicken feet stewed in a savoury sauce. The name of this dish, made in different ways at different establishments, is called "Phoenix Claws." The claws are usually not even in the dish! Maybe it should be called "Phoenix Knuckles," which I would imagine still sounds more exotic than chicken feet.