Why does Socrates think that death is not evil and should not be feared in the Apology?

The Apology of Socrates by Plato is an account of the defense of Socrates before the council of Athens, which is assembled as a jury to hear his arguments. His accusers (Anytus, Meletus, and Lycon) claim that Socrates corrupts the youth of Athens with his teachings and shows impiety towards the gods of the state. The text of the Apology is in three parts: the defense of Socrates, the sentencing plea of Socrates, and the closing remarks of Socrates.
In the course of his defense, Socrates does not exactly say that death is not evil, although he does emphasize that it should not be feared. Instead, he makes the argument that to fear death is not wise because although most people think that death is an evil thing, it may in fact be something that is a great good.

For this fear of death is indeed the pretense of wisdom, and not real wisdom, being the appearance of knowing the unknown; since no one knows whether death, which they in their fear apprehend to be the greatest evil, may not be the greatest good. Is there not here conceit of knowledge, which is the greatest form of ignorance?

Socrates then goes on to say that if he is given his freedom, he will never cease from the teaching of philosophy, as he cares more about wisdom and truth than the threat of punishment.
Later, at the end of his defense, Socrates brings up again the issue of whether or not he fears death, but he remains ambiguous about the answer.

Whether I am or am not afraid of death is another question, of which I will not now speak. But my reason simply is that I feel such conduct to be discreditable to myself, and you, and the whole state.