One word- Jealousy.
Morgoth and Sauron were victims of their own envy in my opinion. Melkor's reason for destroying his fellow Valar's creations was because of that envy. I believe this envy slowly turned to hate, and fed his hirst for power. It's only fitting that the Vala with the most power was the one to fall - like a Lucifer representation in a way. This goes back to the well-known theme of power corrupting. Melkor believed he had some right to the throne of Arda, which perverted him to the point of anger and jealousy.
For Sauron I would just say that he was victim to the deception of Melkor. I believe Melkor created the emotions of hatred, fear and envy, and passed it on to his servants.
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"'Eldest, that's what I am... Tom remembers the first raindrop and the first acorn... He knew the dark under the stars when it was fearless - before the Dark Lord came from Outside.'"
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