The reason that is the vital point lies in the fact that White can answer the atari of with . Without in place, Black would capture three stones.
As said before, expanding the eyespace is not right. Black plays atari at and after , Black can start a ko with at . Life in ko is not sufficient.
This shape does not call for the 1-2 point. The points a and b are miai to keep White down to one eye, and Black destroys the other eye by playing .
Playing at b also works. Black should not play the atari as in the previous diagram, because that permits ko. In fact, destroys more eye shape than it makes and she dies unconditionally.
After here, Black can kill unconditionally, without a ko. After , White cannot make a second eye due to shortage of liberties. If at , at is a deadly eye shape destroyer.
ChaoSpectre: White 1 here doesn't work either... although I'm not entirely sure of it.
unkx80: is good. is death in gote. is also a wasted move. So and cancel out. =)
This doesn't work... but I'm almost certain this isn't optimal play from White 1 for white. Any takers? Just prove it doesn't work at all! ;)