How we cite our quotes: All quotations are from Star Trek II: The Wrath of Khan.
Quote #1
KHAN: You are in a position to demand nothing, sir. I, on the other hand, am in a position to grant...nothing. What you see is all that remains of the ship's company and crew of the Botany Bay, marooned here fifteen years ago by Captain James T. Kirk.
Khan pushes this as the reason he wants to get even with Kirk, and it's a good one. But it's not the only one. There's his wife, for starters, which is the real purpose of the exercise and which slithers out in the odd line or two.
Quote #2
CHEKOV: You lie! On Ceti Alpha Five there was life, a fair chance!
KHAN: This is Ceti Alpha Five! Ceti Alpha Six exploded six months after we were left here. The shock shifted the orbit of this planet and everything was laid waste. Admiral Kirk never bothered to check on our progress. It was only the fact of my genetically engineered intellect that enabled us to survive!
Yeah, that would make us cranky too. We're not saying that what Khan does is right…but he's definitely got a legitimate beef.
Quote #3
JOACHIM: We're all with you, sir, but consider this. We are free. We have a ship and the means to go where we will. We have escaped permanent exile on Ceti Alpha Five. You have proved your superior intellect, and defeated the plans of Admiral Kirk. You do not need to defeat him again.
KHAN: He tasks me. He tasks me and I shall have him. I'll chase him round the moons of Nibia and round the Antares maelstrom and round Perdition's flames before I give him up.
First of all, shout-out to the Moby-Dick quote here, which Meyer set up by showing us a copy of the book itself on the Botany Bay. More important, it reveals another possible reason for revenge beyond the dead wife thing and the exile thing. It's plain old-fashioned ego.
Kirk beat Khan, and Khan is not a man who likes to be beaten. So he's coming back for the grudge match, just to show Kirk who really has the biggest stones in the universe.