I’m just going to think out-loud here, but I think it has to do with what you mentioned, our consciousness and self-awareness. The depth to which we can contemplate ethics, and the death of ourselves or others is unmatched in the world. That is in itself a very unique thing that separates us from the rest of the animals roaming about. A wolf cannot know what it is to die or to suffer like a human can. The idea that we are created by God, and therefor have natural rights (because we are essentially His property) could be considered in the reverse sense: If, we being uncreated (no creator involved) have no rights by our very nature, then God also has no rights by His very nature (being uncreated). Isn’t that wild? I could be wrong, but interesting to think about.