No, Rob. In a pair consisting of human and dog or human and horse, the human is always the master.
With a human and cat, the cat is the master, and knows it.
No; it isn't anything to do with status: it has everything to do with communication.
A cat knows nothing about communication outwith its own species. Don't forget: we had a pack of them, about twenty-something at once. Each had a name, each had a personality, but not a one was able to communicate like a dog can. Of course, it could be that my Spanish wasn't good enough.
Cats know about killing, they know about death of other cats in the mob and they know about rape. Of course, if doing like their big cousins do, biting the nape of female necks and holding them there isn't a forced relationship, then I withdraw the bit about rape.
:-)