The division isn't so clear to Khan - Section 31 is merely an extension of Starfleet, in his mind, a neither acting without the approval of the other.

But it doesn't matter, because as soon as the question is out of the doctor's mouth, Khan is abruptly stilling, posture ramrod-straight and fists clenched. "My crew is dead," he says, words slower and diction crisper for all the plain grief and fury behind them. "They were murdered in their sleep by Commander Spock."

And here, now, he feels more hatred for Spock than he ever did Marcus. The Admiral was a despicable creature, low enough to exploit Khan by using his family against him, but ultimately still afraid of the augments - too afraid to go through with killing them, as he had threatened so many times. Spock, however, had done just that, beamed over the bodies of Khan's sleeping family and let them explode in the belly of his ship.

He'd wanted to kill him. But with the Vengeance crippled, he'd taken the next best option - destroy the institution that had enabled their deaths. Go down with his ship, and be with his family at last.