I have a responsibility to treat him and my dog (a white and brown Jack Russell terrier) kindly, to return the love they give, and to take care of their needs.
That said, I ain't giving up my steaks.
You have identified the key issue in the question of whether animals have rights. I believe that animals should be treated as humanely as possible (I support medical use of animals but oppose testing cosmetics on rabbit's eyes, for example). But that is not because of their rights (they have none) but because of our obligations to them.
When I encounter someone who believes in animal rights, I ask them to imagine that every vestige of humanity was magically removed from this planet leaving everything else intact. Would animals then have rights? Would the little fish have a right to be left alone by the big fish? Would the antelope have a right to insist that the lion leave him alone? Even if they had some theoretical rights, they have no capacity to claim or defend those rights, or even the capacity to understand the concept of rights. In this scenario, the notion of animal rights is ridiculous. Adding humanity to the scene does not endow animals with rights that they would otherswise not have.
I do accept, however, the biblical concept of treating animals humanely. That makes the treatment of animals a matter of my obligations, not their rights.