Let's face it: if someone exiled you on a desert planet and the woman you love had her brain eaten by ear worms while you were down there, you'd probably have a hankerin' to hunt down the guy responsible.
Khan's gotta express some rage (they don't call it The Wrath of Khan for nothing), and frankly, he's not entirely without cause. Of course, there was that whole "I'm going to kill Captain Kirk and steal the Enterprise" thing back in the day. But as we know from literature, revenge has a way of biting the avenger right in the butt…
Questions About Revenge
Why can't Khan just let Kirk go? What is it about his temperament that makes doing so impossible (even though he'd probably be much better off)?
When does Khan's thirst for revenge help him? When does it blind him to the threat that Kirk represents?
Is Kirk looking to get revenge on Khan? Why or why not?
How does Khan modify his revenge throughout the film? Does that mean he might have been willing to let it go at some future point?
Chew on This
Khan's thirst for revenge allows him to escape Ceti Alpha Five and free his followers.
Khan's thirst for revenge is the tragic flaw that ultimately destroys him.