The feeling that it's "sad" if a species dies out seems to be coming from an aesthetic point of view how the world should be. But is there a rationality behind it?
The only rational reason I was able to come up with is that more variety gives more possibilities for study. But this is only a weak argument I think and I hardly believe that this is the reason why most people would like to see these almost extinct animals protected.
And I don't even talk about killings here, or animals in physical pain. Take, for example, George, who died a few weeks ago. It makes me feel that people don't like these creatures to die because they don't want to die alone when they're old.