Uh, that's not the definition that biologists use. Kingdom animalia includes humans. (along with fish, birds, reptiles, insects, etc.) We're mammals.

Also, a vast majority of people use this definition of the word "animal" when referring to the animals themselves and only tend to use other definitions (which typically ends up referring to non-human mammals or sometimes humans the speaker find distasteful for whatever reason) specifically when contrasting them to so called "civilized" humans.

You can look up the word "animal" in a dictionary and I garuntee you the kingdom animalia style definition will be the first one you see under the noun form of the word with all other definitions (the ones that exclude humans or insects) coming later. Dictionaries typically order their definitions by usage when there are multiple definitions of the same word.