This essay earns at least a silver star.
Exactly why we would strive so hard to distance ourselves from our animality is a large question, but surely the human fear of death figures in the answer.
What we see animals do an awful lot of is die, very often at our hands. Animals resist dying, but, having no conception of death, they don't give it nearly as much thought as we do. And one of the main thoughts about it we think is, will my own death be like this animal's or not?
The belief, or hope, that human death is somehow different from animal death is precious to us — but unprovable.
Whether it is or is not is one of the questions I suspect we're trying to answer whenever we look into the eyes of an animal.