I guess it isn't reprehensible in itself. Taking care of an animal, being assured he gets his/her needs covered and overall notice if it's living a happy life can probably be very gratifying, as a personal level for the pet and as a moral level for the person. In some instances, you establish a bond with your pet (and vice versa), which might point out that it isn't definitively reprehensible as its fate would have been largely different but not necessarily a better one.
There's also the fact that you try healing it whenever it gets hurt or sick, and certain animals (not all) trust their human partner enough to allow themselves to be taken care of, while at the same time greeting them or being their personal bodyguard as a repayment for a lifetime of trust.
There is, certainly, a morally reprehensible aspect of pet "ownership", and that's how that ownership is determined by the human side. Adopting a pet because you're a spoiled person and just wants one to play with it for a bit then ditch it? Physically manipulating your dog (i.e. getting his tail cut because it's more "stylized" that way), or maining it for the sake of convenience (like neutering it)? They sure as hell are morally reprehensible, as accepted and normalized as they might be.
