Ah, I see your point.But we don't. Have a look at the broad dictonary definitions. Many, not all, seperate humans from animals.
If you dig into the science then yes, humans get classified as an animal but in common usage the word animal does not include humans.
I am tempted to make a joke about 'common' usage (as someone who is the servant to a bunch of chicken-Princesses), but I won't go there.
Instead I will settle for quoting Midsummer Night's Dream: Lord what fools these mortals be