Why send a manned mission when a robotic one could do just as well and much cheaper.

Armageddon and Deep Impact used human crewed spaceships for dramatic effect, but
automated missions would be cheaper, easier, and safer in reality. What would a human
crew do to deflect a space rock that a robot couldn't?

NASA has already shown concern for such a potentially disastrous situation. Any astronomer
worth their salt can detect and predict NEOs that might threaten Earth. The films I mentioned
where only one or two astronomers found an NEO and no one else could until they were
practically upon our planet is nonsense.

And yes, I am aware that some NEO have gone by Earth and were not detected until after
the closest pass, but that has changed and any ones big enough to do real damage will be
seen long before they arrive by numerous astronomers. That gives us plenty of time to set
up some robotic method of exploration and deflection - no oil riggers turned astronauts
planting a single nuke need apply.