But animals are closer to the environment they live in. Thanks to trade, humans can live almost anywhere and still have access to food, water, and housing. The animal population in a certain area will drop if it's short on resources or there are more predators than prey. There's really no danger of there being an animal surplus [especially if we cut down forests].
Yeah, the only animals that are essential to us are the ones we eat, but we wouldn't raise them on farms if we weren't going to eat them. We control how many of them there are--shoot them up with hormones if we want more of them, increase the number we kill in a day to cut down their numbers, and I bet we would start eating animals that we normally wouldn't eat if someone came up with a convincing enough ad campaign.