On Enterprise, Khan said he tried to get his people out by placing them in the torpedoes, was found out, and had to escape. His actions having been found, he was under the impression his people were then all killed. So he described his subsequent actions (bombing, attack on meeting) as him responding in kind for what was done to him.
Something like that. I thought one issue with the script was the haziness of what the threat was actually supposed to be, and what the bad guys were actually trying to accomplish.
Marcus wants to militarize Star Fleet by starting a war with the Klingons (I guess). And the movie wants to be about avoiding that and maintaining the original goal of exploration, with the 5-year mission starting at the end of the film.
But war with the Klingons never felt like a real possibility, and I don't think the "risk" of militarization, or why this would represent an important change, was ever really established. I guess I'm just supposed to automatically understand why this is bad/different as a longtime fan.
Khan's motivations this time around are revenge... on Marcus. And then he will continue to do other bad stuff. Kirk initially wants revenge, but opts out of that as part of his maturation. Spock is out for revenge after the "death" of Kirk, but snaps out of it.