You don't compete with cats for resources, and you interact with them entirely on your terms. Once an animal enters your life without asking, and reduces the resources available to you, they become 'vermin', and people will do extraordinarily cruel things to them without feeling the slightest pang of guilt on the basis of that same 'superiority' which you feel towards cats.
Exactly- which means that the issue it's not the sense of (even genetic) superiority per se, but that of being threatened.
Btw, we have an entire genre of fiction (a subset of science fiction) in which humanity is threatened by technologically and cognitively superior races coming from other planets- this doesn't prevent us from trying to exterminate them to ensure our survival.
On the other hand, I am pretty convinced that my genetic inheritance makes me "superior" (in some vague, but obvious way) to a cat- and yet I've never harmed or desired harm for cats- I actually like them. Or, to make a different example, while we consider it unacceptable to think of race X to be "superior" to race Y, we have no particular issues in admitting that the individual Albert Einstein was "superior" (again, in some vague way) to many other individuals (us included)- and yet from that doesn't follow we mean those individuals any harm or disrespect.