In this movie, a comet miles across is headed toward Earth, sure to cause a mass extinction if it hits. Astronauts attempt to blow it up but instead split it in two. One piece a mile across hits our planet and causes devastating damage (which is eerily and nightmarishly accurate). The other piece will still wipe us out, so the astronauts sacrifice themselves to destroy it, shattering it "into millions of pieces of ice and rock, which burned harmlessly in our atmosphere."
However, the problem remains: Those pieces would still kill us all! The impact energy of a comet depends on its mass and velocity, neither of which changes when you blow it to smithereens. All those comet bits burning up would lay waste to our planet. Instead of hitting in one piece, you get a bazillion little pieces dumping their energy into our air, which if anything spreads the joy around even more; some scientists argue that letting a big rock hit intact may be better! But honestly, either way--especially with a rock 5 or more miles across--it doesn't matter if it hits intact or in pieces. Dead is dead.
A better solution would be to push the whole comet gently out of the way, but that makes for a dull movie climax. Sometimes real life isn't as exciting as cinema. Thank goodness!