Shortage of liberties prevents White from playing at . Thus White is left with a false eye.
Black does not play at for a peep because White would play at and live. ( and are miai for the second eye.)
captures one stone, but leaves White dead. The points a and b are miai, meaning that the eye is false.
is part of the solution, but if is played as shown in this diagram, we end up with a ko instead of an unconditional kill.