Thanks for writing. You raise a number of provocative questions, which I'm glad to try to engage.
First, on the question of "humanness," as addressed in your last paragraph (Parthian shot?). I don't, alas, equate the "human" necessarily with the good, the true, the beautiful, or even with Matthew Arnold's "best that can be thought and said." There are lots of kinds of human activities that seem to me distinctly ignoble, though there are at least as many that are noble, selfless, elegant, gracious, etc., etc. Human--for me, that is to say--is not necessarily a synonym for "humane." This is a point vividly made by Lord Byron in his epitaph for his beloved Newfoundland, Boatswain, whom he described as possessing "all the virtues of man without his vices."
History contains some distinctly less than admirable characters who loved their dogs. Consider Cincinnati Reds owner Marge Schott, censured by organized baseball for her racist remarks about blacks and Jews, but equally famous for her adoration of her Saint Bernard, Schottzie. Schott once professed herself something of an admirer of Adolf Hitler, remarking that he "was good at the beginning, but he just went too far." As for Hitler, he cherished his German shepherd, Blondi, for whom he commissioned a bombproof kennel. "Inhuman" behavior and "humane" sentiments (in the modern sense of animal protection) can, that is to say, occasionally coexist. When I say in my book that "it's the dog that makes us human," I mean not necessarily that dogs make us better people, but that dogs mirror, reflect, elicit, and even model "human" behavior and "human nature" in the minds and imaginations of humans.
But about "humane societies" in particular: You ask, trenchantly, whether the rise in visibility of animal rights causes in recent years suggests to me that we are becoming a more humane society. One could make the opposite argument. Like laws and regulations, rights activism often arises because there is some infraction or violation. We develop regulations against jaywalking (nice buried avian figure of speech) when people jaywalk and risk their own safety or that of drivers. So the increased visibility of the animal rights movement may well be a sign that the perceived rights of animals are in need of safeguarding (more animal abuse, more laboratory testing on animal subjects, etc.). In other words, what you describe as the "great momentum animal-rights causes have enjoyed in the last 20 years" might suggest that some people are becoming "more humane" because other people are behaving less humanely.
"Humane society" itself is a term with a curious history, as I note in Dog Love: It originally meant a society formed to rescue humans (e.g., drowning sailors) by using trained dogs, especially Newfoundlands and Labradors. The idea that humans need to organize to rescue dogs and other animals from human mistreatment eventuated, in the 19th century, in the formation of groups that originally called themselves "anti-cruelty": in Britain the Royal Society for the Prevention of Cruelty to Animals, and in the United States the ASPCA. Even today some colorful characters in British fiction use the shorthand phrase "the Cruelty" to denote what we would call the Humane Society, as in "I reported the abused dog to the Cruelty." So--to get back to your question--it could be said that the rise in animal rights activism comes about not because we are becoming a more humane society but because cruelty to animals has not, despite many people's strong efforts, disappeared as an aspect of human behavior, even socially sanctioned human behavior. On the other hand, it might be contended that rights activism in general has become more visible in the last 20 years and that animal rights are part of that development.
From this rather somber subject, let me move on to another of your points. I agree with you in general about some of the problems with anthropomorphizing dogs and cats (my dogs don't own denim jackets or pajamas with feet or rubber boots or any of the other cute humanoid items obtainable at upscale pet boutiques), but I'm not completely convinced that they have "truer natures" in an absolute, species specific, sense. Once culture enters the picture, as it inevitably does with any domestic animal, the nature-culture division itself becomes of necessity blurred. Why would dogs associate the rustle of plastic bags (for scooping) with the promise of a walk, or the jingle of a chain with the presence of another dog? The domestic, that is to say, is itself a "humanized" category. Moreover, dogginess seems quite variable, breed by breed and dog by dog. Just as "boys will be boys" seems a phrase calculated to raise hackles (whoops, what's the obverse of anthropomorphism? can your hackles rise if you don't have any?), so assuming that dogs will be dogs has some limits as well as some usefulness. In saying that you'd rather be described in cat clichés (graceful, intelligent, elusive) than dog ones, you list human clichés about dogs like subservience, malleability, and predictability. But one could just as readily produce some antithetical clichés. In our conversation about the gendering of cats and dogs in popular culture, for example, we might have talked about "tomcatting around" as a (negative?) stereotype of human male sexual behavior. Or about the fact that two of the most familiar dog names are Fido ("faithful") and Rover.
Of course, the question is indeed one of cliché and stereotype: It's human fantasies about dogs and cats, as much as what they are "really" like, that lead, not only to the creation of dog and cat fictions in human culture (Jack London novels, Krazy Kat cartoons) but also, as you yourself imply, to the social engineering of breeds to conform to our human desires. The overbreeding of "Lassie dogs" after the success of the Lassie films and TV show in the 1940s and '50s and the appalling adoption and subsequent abandonment of Dalmatians after the success of Disney's 101 Dalmatians are one kind of example, but so, perhaps, is the "blonding" of golden retrievers in recent years. Do blond dogs have more fun?
I look forward to more.