I'm not talking about giving rights to the animal and I'm not calling you a prick, I'm talking about the rights of the pet owner in a make believe libertarian world.
In said world, I could kill your cat, and by law, would have no criminal charges against me, and would probably only have to reimburse you zero dollars for the cat considering you adopted it, and if you're very lucky maybe some of your vet fees. But really, you wouldn't even bother with taking me to court considering the low potential of significant reimbursement.
So, I could kill your cat and effectively nothing would happen to me, and you would just have to replace it. It's just too bad you spent a small fortune fixing a cheaply replaced commodity.
Considering you say you love your pet, me killing it would probably cause you great emotional stress, but this would be irrelevant as it's only a commodity which can be replaced. You don't have the right to claim you have suffered emotionally, even if you genuinely have, because that doesn't exist in this world. Is that freedom for the typical pet owner? Someone else dictating to you what your pet means to you?