It's simple economics. We don't extend legal rights to other species because we can't afford to extend them to everything right now and we consider other things higher priority. We have some wiggle room on how much we could invest in this (for instance, we can bring up dolphins), but we definitely cannot afford to encompass every species at this time.
There isn't really an absolute moral reason to not extend those rights to other species. If everything, it's the opposite, if we could actually afford it.
Incidentally, I think all rights are stuff we make up and not intrinsic in any way.