White does not want to play at the upper left corner, because that would give black a fourth eye. So white persists on the right.
White should also begin with . Black must respond, or his stones will die in a collapsing seki. (Variations given below)
However, is a powerful tesuji. (In fact, it is so powerful that even the creator of the problem did not realize how powerful it was.)
Notice how removes also the 2 black stones. Also note that a black play in the lower left corner would have self-captured black's main group too.
Now it is important to notice, that black can always "waste a move" in the upper left corner, that is, he can play there, and end with sente and an eye. This enables black to kill: