I mean the obvious parallel to slavery, they are property owned by somebody who are not truly free to leave and have been bred to the point of dependence, are regularly neutered, are leashed regardless of need, they are commonly fed kibble produced from waste not fit for human consumption at rendering plants, and so on.

I'm not saying there couldn't be I don't know, a pet owner who took them in off the street or from a shelter, nursed them back to health, and are lifetime companions in a consensual idealised relationship, with the ownership mostly being a legal technicality. Yet there is an ethically dubious side to pet ownership which I could imagine getting the entire institution framed in a negative light in the distant future.

I imagine in the year 3000 there might be a future where schoolchildren will be shown holograms of rendering plants and told by the teacher "And this is what they fed the animals" and then a Labrador Retriever will have an AI write an essay which states that "the ownership or consumption of any animals, is fundamentally a crime against animal rights".