Well, I don't wish to sound unsympathetic, but if the cat has a right to be in the cabin and the owner has paid for that, then technically you're the one with a problem, so it falls on you to make the choice about what you want to do, exit the plane, or fly.

It's a little bit of a stretch, but your complaint could conceptually fall in the same category as someone who objects that there's a crying baby seated near him/her. You may find it objectionable, but you don't have the right to have the child removed.