I just don't understand it.
Of all the characters on the show, Carl is the only
one who's adapted to the new world and
continued to be a good person overall. The kid he killed deserved his fate; not only did he fail to follow the instructions of three gunmen in a time of war
, but he was acting in a threatening manner. It was clear he was going to try to pull something, seeing Carl as an easy target, and Carl -- rightfully -- pulled the trigger in order to protect Beth, Herschell, and his sister, all of whom were placed under his protection. If a fight between the two broke out, there was no way Carl could triumph physically, so pulling the trigger was his only option. There's not even any room for a valid argument against him doing so aside from the writer's trying to force the issue via Herschell's inane "killed him in cold blood" bull.
Just take at look at what he did when he discovered Tyrese's group. He didn't go all psychopath and murder them, and he certainly didn't leave them for dead with the zombies. He brought them back to the safe area and put them in "protective custody" until his father returned in order to deal with them. He even talked with them like a reasonable human being, explaining why he did it, and offering them amenities for the duration.
When he killed Shane, he did it to protect his father. When he killed his mother, he did it to take her out of her misery. And the few other times he offered a solution to a problem, is what a completely rational and sensible plan. A bit cold compared to our non-apocalyptic views
, but completely understandable considering the world he's in now.
He's fully accepted what the world has turned into and is dealing with it far better than anyone
else on the show. And he sure as hell isn't a psychopath like Merle or the Governor, or even the Governor's cronies (one of which, at least, also seems to be more rational about the situation).
Daryl's about the only one close to Carl's level of acceptance, and even he is still holding on to hope of the way things were a little. Carl's just put the past in the past and is doing his best -- as a friggin' kid no less -- to keep his "tribe" alive.