I attended a talk in college by a guy who had measured a bunch of cultural attitudes toward animals, nature, the environment, etc. from different cultures all around the world, then ranked them from most empathetic to least empathetic.
He found the #1 contributing factor to be whether or not that human population coexists with monkeys.
Monkeys are the link that connect us to the animal world. Looking at the face of a creature that is similar to your own is tremendously powerful.
I think it's natural to wonder about our place in the world, but you're right: we shouldn't think of ourselves as distinct from it.