Learning of or seeing signs of death, any death, always makes life seem so much sweeter. I think perhaps the reason that people are upset by seeing something die or hearing of something dying is because, in its own way, sight or news of such things reminds us that we are in fact mortal and, one day, such a fate will be ours too.
That, and knowing how much we ourselves love life, are saddened to know that such joy has been extinguished within another creature that, only seconds prior, was as alive as we.