First, we would need some time to get the experience to reach that rock.

Then, considering the effort spent acquiring experience, it would be better to focus on a large asteroid.

In fact, it would be even better if we could find a way to spare some of the effort to put it on a stable earth orbit.

Wait then, couldn't we put this big rock already in stable earth orbit called "the moon" to some good use?? It's not like we've never been there tens of years ago!!

EDIT: gravity and chemical composition are valid reasons to mine an asteroid, you are totally right. Yet if we wanted not to mine but to have a colony to edge our bets for a meteor strike, IMHO the moon seems to be a better choice. However, I should have been clearer with my thoughts, I stand corrected :-)