Scar needs no backstory. He's the unlucky second son in a monarchical system of male primogeniture. From the day he was born, he was an after-thought. Mufasa need not do anything wrong and Scar would still have been resentful. And unlike in a human monarchy, where the second son could be a high-ranking bishop, general or diplomat, what role is there for a beta male lion, other than to skulk and become jealous?
Yes, sometimes I have fun evaluating Disney royalty by real-world rather than fairy tale standards... I've come to the conclusion that Elsa in Frozen is Disney's worst monarch, although she does much better in the sequel.