It seems to be the grand irony that animals MUST not suffer and die in movies, even as billions of people perish all around them.
It reminded me of one of my earlier posts where I asked what it says about a society that spends billions caring for pets while letting children starve. "Flames" picks up on this same trend in disaster movies; billions of deaths don't bother us as long as the dog survives.
In a way, it all goes back to Noah, and I wonder if the story of his ark paves the way for this double standard of carnage. In the story, Noah, and the readers, accepts as given that humanity is toast. God has decided on the flood, and it's going to happen. As a result, our full attention turns to saving what little can be saved; Noah knows he'll have his hands full with the animals and his family, so he writes off the rest of humanity and leaves them to the water.
Disaster movies bring that same sense of acceptance, and, in fact, reinforce the lesson to the audience. Characters that try to save everyone get killed by the unstoppable disaster du jour. Usually they die as heroic martyrs, but they still die. Of course, those who selfishly think only of themselves also die. The trick is to be selfish but not too selfish; be just selfish enough, and remember your pet. Horror movies, on the other hand, teach us never to go back for the cat, but that's a different story.
Is that the problem we face? Are we trying to find that line between being generous and being too generous, or do we really care more about the cute animals dear to us than the humans we don't know? I'll optimistically assume it's the first one. That gives me a chance to help people draw their line somewhere farther away from home than the doghouse.