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.

Only in the sense that it's impossible for you to be a rock, or a tree, or an alien, or another person, because you clearly aren't any of those things. All this tells you is that you should be nearly 100% certain that you are you, and that's no great insight.