Considering the vast number of non-human animals compared to humans, the probability of being a human is vanishingly low. Therefore, chances are that if I could be an animal, I would be. This makes a strong anthropic argument that it is impossible for me to be an animal.

The anthropic principle creeps in again here, and methinks you missed it. The ability to make this argument is contingent upon being an entity capable of a certain level of formal introspection. Since you have enough introspection to make the argument, you can't be an animal. In your next million lives, so to speak, you won't be able to make this argument, though someone else out there will.