White can't play at the marked point because of shortage of liberties.
After , instead of White can play at a or b to live. (But here in terms of points may be the best move.)
The stones turn the hane at into an atari to which White must react, so that Black can take away the second eye with .
Enlarging the eye space at invites Black to play at the vital point . Now and are miai. After , White has to prevent the capture and take a liberty at a upon which Black takes away the other eye at b.
Connecting at in this way makes poor eye shape. Black plays on the vital point of this shape. Even if White continues with at a, Black will be able to almost fill her eye space with a farmer's hat.
Connecting at here is symmetric to Failure 4 and is once again countered by playing on the vital point.
TwoSpaceNotchersNotFullyConnected has analysis of a shape that behaves just like this problem; there is some overlap with this SL page.
Here is a similar position:
In this symmetric situation, both legs of the white group have no liberties outside of the eyespace. Now a move at a or at b will be answered by a move at the point diagonally underneath. White is dead. (But compare Problem 23.)
This shape is analysed in its own page on SL: Flying Saucer Shape.