I also find it helpful to recall one of the simple arguments from earlier,

If one is a cat, then one is also a mammal (C → M), meaning that being a cat is sufficient for being a mammal is necessary for being a cat.

Denying the sufficient in this case would be like saying that since animal X is not a cat animal X is not a mammal, a claim whose validity is not guaranteed since animal X can potentially be a pig or cow or dog, etc. All of which are still mammals while simultaneously failing the sufficient condition of being a cat.