I’m not sure whether the intention is to determine one’s favorite species of animal or one’s favorite particular individual animal. I’ll presume the former as the latter would turn it into a “Which of your pets (or children — for those who count humans among the animal kingdom) do you love best?” type of question — which is awkward to ask anyone with whom one is not on intimate terms.
At any rate, I’ve come to think of assigning favorites as a bad habit of lazy minds, intended to negate the need to actively observe and to see the beauty and brilliance of whatever stands before one at any given moment. [It’s part of a vast array of patterns people develop to be as cognitively disengaged as can be managed.] So, I don’t have a favorite species of animal, but aardvark does come first in the dictionary, if not in my heart.
[Incidentally, when I had multiple pets, I did have a favorite, and — perhaps tellingly — it was the one whose personality was least like my own.]
Tiger Riding for Beginners 