The Day After Tomorrow violates the Dog Rule.
Simply stated, the Dog Rule holds that no good movie seeks a larger emotional response from the survival of a dog than from the casual death of a dozen or more people.
The rule was devised after watching an earlier Roland Emmerich opus, Independence Day. In that film, evil space aliens attack the earth. The audience sees New York City and Los Angeles destroyed. While little of this mass destruction is on a human scale, the explosions and fireballs make it clear that millions of people have just been killed and that the audience may be witnessing the highest-ever cinematic death toll (depending on how many people lived on Alderaan).
Then Emmerich cuts to a highway tunnel near L.A. where Vivica Fox, a cute little kid and a golden retriever are trapped in an unmoving line of cars attempting to flee the city. Fox and the little boy duck into a maintenance tunnel just as another fireball shoots up the road, casually dispatching hundred of people still trapped in their cars. In slow motion, we see the golden retriever leap to safety and the audience cheers.
Years later, Emmerich is still making global disaster movies. At the close of The Day After Tomorrow, the President Cheney character provides voice-over narration, explaining that, despite the devastation of most of North America and Europe and the death of untold millions, everything was OK because the handful of survivors in New York City includes our protagonists. We then see them rescued from the roof of the NYC library — including a brief closeup of, of course, the offending dog. (To the audience's credit, they groaned.)
The worst violation of the Dog Rule that I've seen was probably in Pearl Harbor, which dealt with a historical event and recreated the actual death of more than a thousand actual people. Yet as Michael Bay and Jerry Bruckheimer's version of the U.S.S. Arizona sinks beneath the waves, the camera focuses on one doomed sailor's dog, leaping over the side and swimming to safety.
Pearl Harbor tried, and failed, to recreate the success of Titanic. Say what you will about James Cameron, he at least had the decency to show the dog drown too.