1
there are actually people that do identify as an animal and cats are one of the most common. They still acknowledge that they are still human. It's generally spiritual, phycological, or both. It's known as alterhuman. This is an actual identity that people do take seriously so please do not assume it is a joke. However, many trolls claiming to be alterhumans do get mistaken for actual alterhumans. The specific term to describe one that identifies as an animal would be therian.
2
A cat is only used to help describe the gender. It does not mean you identify as a cat or saying your gender is a cat. It is generally used as an analogy, help describe how the gender feels, or other ways to help describe it.