It's not so much immortality, save among a handful of my cousins, as it is an obscenely long lifespan. When even the supposedly immortal elves end up dying long before you're even feeling the first twinges of age, it can get a bt depressing if you don't adapt.
Of course, there's also the simple fact that, let's face it, othe races are little, soft, and weak in comparison. We're solitary and generally carnivorous by nature. We don't tend to keep pets, and that's about what the average mortal amounts to... Sometimes a vicious, bloodthirsty, feral pet, but pets still.