Why did Dumbledore let Snape kill him? ... He wanted Snape to remain a trusted member of the Death Eaters, as well as to prove Lord Voldemort his loyalty and show him that he hadn't failed. Also, being familiar with the fact Lord Voldemort has ordered Draco Malfoy for killing him, Dumbledore wanted to protect Draco's soul.

Did Snape really betray Dumbledore?

In return, Snape secretly allied himself with Dumbledore and the Order of the Phoenix as a double agent against Voldemort, using his powers of Occlumency to hide his betrayal from Voldemort. ... Even with his efforts to protect her, Snape felt responsible for Lily's death at Voldemort's hands.

Why did Severus Snape turn bad?

Snape as a person was not very friendly or social, for that matter. His anger had a lot to do with his troubled childhood. He was a halfblood, had parental issues and was thoroughly bullied by James and Sirius at Hogwarts. This led him to develop a tough exterior.