> why don’t animals have rights?
I believe it's self-evident that there is something in our brains that causes us to mentally separate things into in-group and out-group. In other words, we evolved to be social and generous, but only tribally so. Visual and behavioral differences such as skin color and culture can be the difference between in/out-group delineation. And so it is with animals. They are so similar to us and have so many of the traits that make us "human" that it's obvious they should have certain rights, if you think about it. In fact, some animals do enjoy rights to be protected against humans, as cruel treatment of animals is ostensibly taboo in Western cultures as long as you ignore current American factory farm practices, and in the case of some protected classes of animals such as dogs, enforced by law. But the differences between humans and other animals is enough to trigger the in/out group delineation, so almost no one bothers to recognize they should have rights, let alone fight for them. Those that do fight for those rights are typically relegated to the out-group themselves.
In short, it has nothing to do with logic, and everything to do with the primitive parts of our brains running the show.