It's only logically inconsistent because you omit context and over simplify to suit your argument. There's no trace of culture or law in your argument.
I am willing to explore this argument with you, but at my first glance it seems your more interested in being right, and the argument itself, than being able to admit that it's not as black and white as you would like it to be.
There's a difference between pets and animals for eating.
First of, people are expected to care, protect and even love pets. You have bought the pet, not for eating, but for something like companionship. If you show total disregard for the cultural rules and norms sorrounding pets, people are going to be upset. You are expected to care for the animal - also by law.
It something way different if you hurt a pet than if you slaughter an animal that was brought up for the sole purpose of being eaten.