Well, I don't think we recognize a general right to life for animals, even for those protected under the law. Euthanizing a cat or a dog is allowed virtually everywhere, unlike a human, for example. We certainly don't recognize any right to bodily integrity for animals, as even cats and dogs are routinely sterilized.

Generally, we instead have animal welfare laws that protect various animals to various extents for various reasons, based on human interest in said animals (e.g. You can sterilize any cat you find, unless it's owned by someone else, but you can never shoot a cat; you can shoot many wild animals within certain limits, but you can't sterilize them outside very special circumstances).