My feeling here is that the only reason this question should come up is if there's confusion about what slavery is. So if it did come up, it'd be important to explain the nature of slavery versus pet ownership:
1) It sounds like in the OP's case, we're only talking about books in which the owner is an anthropomorphized animal, clearly a stand-in for a human being (I have heard of an upcoming picture book in which a pet wants to own a pet, but that's another story). In cases such as Arthur, the fact that they're animals doesn't even affect the story. They're treated as people. I get the concern here because sometimes it weirds me out too, but the difference is the nature of ownership and the level of sentience of the pet. Owners and pets in these examples may all be animals, but they're also clearly in different stages of evolution, and in most cases they're also different species (So are you saying that enslaved people are on a different evolutionary track than their owners? See the slippery slope here?). It's worth noting that while Mickey Mouse owns a dog, Goofy doesn't own a dog.
2) Pets, in general, are not oppressed (and to be clear, I'm not talking about animal cruelty, which is a real and separate issue). They do not perform intense physical, mental or emotional labor for their owners (I'll make allowance for livestock, barn cats, working dogs, etc. because they do perform labor, but should be noted that these are not always "pets"). They are not treated as financial assets. They do not have basic human rights withheld because they are not humans. They are animals. My cat, for instance, can't sit at a table and eat from a plate with a knife and fork because she doesn't have opposable thumbs. Their anatomy is also different, and it's much more natural for a cat to eat from the ground (which they have evolved to do) than upright at a table.
3) To expound on this, the relationship of pet and owner is often symbiotic. I receive benefits from owning a cat; companionship, stress relief, entertainment. My cat also receives benefits from me: companionship, food and shelter, healthcare, entertainment. Animals, too, form symbiotic relationships in the wild; wild animals (like birds and dolphins) even form symbiotic relationships with humans! This is still not the same thing as slavery.
4) Comparing slavery to pet ownership is like comparing human beings to animals. People of color have a long history of being considered less than human; this is a stigma that we're still fighting today. Associating slavery with pet ownership trivializes the real and damaging horror that is the human slave trade.
So, if anyone DOES have concerns about whether animals owning animals resembles slavery, these are things that should be considered. Pet ownership and slavery cannot, and should not be treated as equal. To do so is to imply that enslaved human beings are of lesser intelligence to their owners, and we don't want that!