Cougar goes a little tense when Jake says what he does. He knows that Jake deserves that kind of life and that kind of happiness, but he's selfish because that means he has to give him up. And yet, he would if it meant Jake got to be happy without him. "You're important to me," is his gruff insistence, seeing as that's something keeping him sane.

"You're here," he says. "Calming down the night terrors."

Don't leave is what he wants to say, but he wants Jake to be happy. And if he has to give him up, then he will.