This exercise uses the concept of miai.
is the only way to live, which makes and miai. That is, if White plays at , Black lives with ; if White plays at instead, Black lives with at . The concept of miai is that there are two (more or less) equivalent points, so each player will get either one.
In solving this exercise, this reference diagram is also very useful. It is the same as the problem except with the stones added, so it becomes a basic T-shaped four-space big eye (called the pyramid four), The point a is the vital point. If White plays at a, Black is killed; if Black plays at a Black lives.
With the reference diagram it becomes easy to explain why enlarging the eye space at fails. Even though there is no stone at a, the concept is still the same. So kills the black group.
I leave it as an exercise for the reader to see what happens if Black plays his first move at a instead.