If pushes in, then captures and White only loses stones due to connect-and-die. Note that the capture of gains Black a liberty, so after Black is not under atari.
If plays at the other 1-2 point, then cuts and captures everything. Even when White connects at a, then Black is still alive with the bent four living eye space. at a also lives, but with less points.
The main failure sequence is to atari at , hoping White will connect and then we revert back to the solution main line. But no, with Black can only live by winning the ko.
An interesting variation from the main failure sequence is this and is worth discussing. It tries to combine two techniques: snapback and connect-and-die. Obviously White cannot connect at a...
However, this is not a typical snapback, but rather a case of capture two, recapture one. After the only way for Black to continue is to fight the ko at a.
While this variation sequence does not allow Black to avoid fighting a ko, however it does provide Black with two local ko-threats, namely, and .