All mammals are animals. I don't know what your definition is but it certainly doesn't match up with any dictionary or scientific one.
"In non-scientific usage, any member of the kingdom Animalia other than a human being." (https://en.wiktionary.org/wiki/animal#English)
The lack of definitions, the fuzzy logic is the problem. Yet, I am often amazed by accurate law codes, and I am far more astonished by how wrongly I and others use those words contrary to their original usage. I accept that words are defined by their usage. I cannot accept competing definitions. Point in case, I wouldn't say humans are animals, and historic usage proves me right AFAICR from reading on free will etc. At best, a human is a mammal. But you seem to want to use the word differently, so, I agree that this doesn't really work.