#1. Compare the mass of an ICBM with the mass of a meteor.

and
Now, if the meteor is hit, it will break up into smaller chunks.

Um, I think you're missing something here. The type of force required to disable an ICBM is actually pretty small; you probably wouldn't need to do more than launch a chunk of lead into its path and it would be very likely to disable the weapon. An explosive charge would only be insurance.

Take the size of an ICBM. I don't know exact dimensions, but maybe 3 meters around and 20 meters (I'm being optimistic, the missiles they fit into subs are smaller) in length?

A dangerous asteroid would be 100 meters in diameter; a dinosaur-killer would be much larger. The type of explosives that would be used against an incoming ICBM wouldn't make a dent in a dangerous asteroid. It's doubtful even a nuke would do enough damage to a nickle-iron asteroid to destroy it. And as you note, the ABM defenses would only be catching it as it entered the atmosphere; far, far too late.

All that said, just because there may be a bigger danger from so-called suitcase nukes doesn't mean it isn't worth testing and building an ABM system. R&D into ABM as a concept for missile defense can extend to, say, anti-SCUD defenses and anti-Stinger defenses. I'd think that a laser defense system effective against ICBM's should be effective against a wide variety of other targets.

On the other hand, I personally would prefer to be putting money into cheap access to space. The NASA bureaucracy is so fixated on the shuttle that they seem to be doing their best to scuttle any competition or alternates.