Actually, chimps are more genetically similar to men (nearly 100%) than mice because we've shared a common ancestor in more recent times (whereas our common ancestor with mice lived pretty much during the time of the dinosaurs). This actually is the reason why we value the rights of chimps more than those of mice.

I don't quite agree with you about this lack of correlation: there certainly is at least a weak correlation, and it's possible that it's stronger. However, I agree that it's possible that the reasons are primarily behavioral (we seek to preserve that which acts, or looks like ourselves). But then, behavioral reasons really are just a simplification of the genetic reason: people have no natural way of sensing the genetic composition of other species, so they have evolved to use the closest approximation, and that is observing appearance and behavior of species and acting based on the assumption that those species that act more like us in fact are genetically closer to us than those that don't.