Logan had known that what Karr said about Laura was a lie the moment he said it. Just another senseless lie meant to hurt, or to enrage. For one thing, he would have smelled it on him long before he said a word, for another, he'd see Laura fight, and her claws were bigger than the boy's. Nonetheless, it gave him pause to see how Karr couldn't ever get past that prickly bubble of selfishness of his. It stank of old pain and fear that made Logan want to go after the people that raised him for fucking him up this badly.
Then again, he couldn't deny what his heart knew. Karr was a mad dog, just like his daddy had been. But in Logan's case, the army popped that egotistical bubble early on. They hadn't killed the mad dog, but they had curbed it so that he didn't become this sorry mess his son had. It was harsh, but it was the truth, and Logan wasn't the kind of man to balk at the truth. Even then, Logan had found ways to go off the rails. It hadn't been until he'd lost an eye and a leg that life had well and truly broken him. Being a cripple taught him humility at last. Maybe even humanity. But there were also significant differences between him and Karr. Logan had always been able to see when someone was showing him decency, and his instinct had not been to bite the hand that fed him. He might have snapped a little, but never would bite.
The philosophy underlying his early martial arts training had introduced him to things like meditation, which had also helped quite a bit. Seeing oneself in the harsh light of meditation had been humbling, and healing. But he couldn't force these things upon Karr. Logan had chosen to seek self-awareness. Karr appeared to be too self-involved to even consider that.
A mad dog. Karr showed no remorse. He didn't seem to perceive the difference between right and wrong. It weighed on Logan to think that perhaps his son was beyond saving. It was a possibility he needed to consider, but not now. Karr was way to young to even be thinking that. He could still find his way, he thought hopefully. He could still turn his life around, find tools to keep the raging beast in check. Hell, if Logan himself had, anyone could. Right?
Logan sincerely hoped so, because he knew full well there's only one humane thing to do with a mad dog and, in this case, putting him down would be his responsibility. He couldn't allow anyone else to do it, for Logan might then kill them in his grief. He may not have raised this boy, but he was his flesh and blood and he loved him. He was never going to put him down, not unless Karr did something so heinous, so unforgivable, as to give him no other choice.
It would probably kill him to do it, but he would if he had to, no matter how hard his heart would break.