In The Apology why did Socrates want the death penalty?

First of all, please realize that it is Socrates, not
Plato, who is arguing that Socrates should be executed.  I have changed your question to
reflect that.

Basically, Socrates insisted on being
executed because he thought that was the only choice he had if he did not want to betray
his principles.  He could have, for example, opted to be acquitted if he would give up
his teaching, but he felt that his mission in life was to do just exactly that -- to go
around teaching.  Therefore, it would be better for him to die than to give up the
mission that he had been given by the gods.

Socrates
believed that what he was doing was important.  He believed that it was important for
him to go around goading people into doing right.  He felt that this mission of his was
so important that he was willing to die rather than to give it up.  This is why he
argued that he should be executed.