The classical argument presupposes that humanity falls within the genus animal. If some human were not an animal, an individual would have to be human while lacking what is held to belong to the logical definition of human.
This would jointly affirm and deny the relevant genus of the same individual in the same respect: a contradiction.
The reasoning depends on the substantive logical account of “animal” as part of the concept of human; it cannot be obtained from a superficial resemblance of words.