In this problem, Black cannot live unconditionally. We start off by playing at , which reduces the liberties of the stones by one.
If wants to kill, then the number of liberties of the stones is further reduced by one. This enables to start a ko for life.
Although also reduces the number of liberties of the stones by one, destroys the eye and does not have to reduce the number of liberties of the stones. So Black loses the capturing race.