She had been an innocent girl who's blood stained the beginning of a war that would take his life too. He'd wanted to be her savior that day that Agamemnon took her. Achilles wouldn't forgive him for that, among other things Agamemnon had racked up quite the number on Achilles' hate list.
He held onto her hand softly as a reminder that she was not alone. Never was she alone. And if no one else would stand up for her, he always would. "As long as you know the difference between the two, you are still someone's daughter." Clytemnestra loved her even if Agamemnon lost his way. "Taking a life is never easy. Eventually it catches up..." he spoke with a pained expression. No one knew better than Achilles of the grief in living with what you'd done.