Here's something that occurred to me about four years ago. I saved it to work on for a bit, and never had time, so here goes some preliminary thoughts that will hopeful have more substantial permutations in years to come.
I posit that:
Cruelty to animals is wrong not primarily because of animal nature but because of human nature.
Humans were intended to care for animals. (As part of having dominion. Genesis 1:26-28) Husbandry is rooted in our nature.
Animals are inherently less valuable than humans. (Humans alone have the Imago Dei. Genesis 1:27. God demands a reckoning for man's life, but eating animals is allowed, post flood. Genesis 9:3-6)
When a human acts with cruelty toward an animal, he does violence to his own humanity. He does not degrade the animal so much as he degrades himself. To act cruelly toward an animal is to act contrary to man's nature (how man was created to be, "nature" as distinct from the fallen "condition"). It is to act as an animal, with no regard to rationality or to man's final end (the end sought is a feeling of power or retribution, which, though momentarily satisfying, do not lead to true happiness).
Thus, when we condemn the cruel man, we ought not to focus on "animal rights." An animal does not have natural rights, only legal ones. What is under consideration is not the rights of the animal, but the actions of the man. The morality of those actions has less to do with the animal than which the character of the man. The man has shown himself to be defective in his character; he has acted less than human. He has inflicted pain without cause or reason. His action is reprehensible because it harms a creature he was intended to care for; not only was a creature harmed, but he harmed it, and in so doing, he harmed his own character and violated his own humanity.