I don't think the phrase "the dog must disappear", at face value, is acceptable to animal lovers.
This version might actually appeal to animal lovers:
The dog must disappear from General Motor's vehicle crash testing labs. The cat, like the dog, must disappear from the University of Wisconsin-Madison's animal testing lab.
This version might appeal to animal lovers, because the author's use of the phrase doesn't represent a view he holds:
A utilitarian utopia seeks to end suffering. And how best to end suffering, a utilitarian wonders, than to remove from the earth all things that suffer? In this mindset, the dog must disappear. The cat, like the dog must disappear. The utilitarian utopia is repugnant to those of us who value life. A Kantian argument for animal rights offers a more plausible account of animal rights without falling into for the repugnance that utilitarians find inescapable.
The version might appeal to animal lovers, if they accept certain premises the author believes about the nature of human/animal relationships:
As long the view "pets" are property that humans own and assert their power over, a mainstream animal welfare will never take hold. If we cannot rid ourselves of that harmful view, the principle of least harm dictates that we must rid animals from our homes. The dog must disappear. The cat, like the dog, must disappear.
This version might not appeal to animal lovers, but it might not sound nearly as "extreme" if it were paired up with a persuasive list of reasons which demonstrate how the author arrived at his conclusion:
The dog, as we know it, must disappear. Pedigrees and purebeeds have resulted daschund's who suffer from permanent back problems, mastiff's whose body size causes ulcers along their arms and elbows, pitbulls who are a public danger to people and other dogs.
This version might be tolerable to animal lovers, as long the author tempers his black-and-white with a pragmatic realism:
The institution of "pet" ownership has been a net harm to animal welfare. We cannot undo the harm without removing ourselves from animals sphere of exist. "Pets" must disappear. The dog must disappear. The cat, like the dog, must disappear. This thinking, however, is counterproductive, perhaps even worse than the present state of things. There are millions of stray dogs starving on the street, and millions of homeless animals being euthanized in shelters. We can begin to heal the millinia of harm to animals by re-shaping how think of animals in our care, by adopting them into our homes as companions, not "pets", making them part of our families; by rearing new pups and kittens as additions to our family, not as profitable additions to the commercial breeder's pocket book.
Context matters. There are too many ways that quote mining can distort an author's meaning, making the author appear to agree to views that they don't in fact hold, presenting a controversial statement without requisite context to show how the author justifies their statement, or making an author's view appear more extreme than it really is.
At present, the totality of everything you know about John Bryant's opinions on captured in 3 sentences with absolutely no context. Something he said incorporates the phrase "the dog must disappear". You don't know if those comments, at face value, are representative of Bryant's views. Presuming that they are, you don't know how he arrived at them.
Given the track record that quote miners have with misrepresenting the views of people they quote (
biologists who are secretly anti-Evolutionists,
Climategate,
Peter Singer's critics), I seriously doubt that whoever compiled the quotes had any intention of presenting Bryant's views fairly.
I would be happy to have a discussion whether killing animals is inevitable or ethical, but personally not interested in distracting myself from work any more than I already have.