Violence is bad
I've been participating in a bunch of discussions here, and it seems that a lot of people start from the position that being violent is ok, and that you need to justify why not being violent is right. Yes, this is in regards to Kenny. A lot of people seem to believe that his actions are justified because they are intended to make Clem and AJ safe, but remain oblivious to the fact that Kenny puts Clem at risk.
What I want to get across, however, is that while some violence is necessary, it will more often put people at risk rather than make them safe.
Let's start with when they're captured (although you could go even further back). In the truck, he tries to free his hands. His plan at that point was to punch one guy, take his gun, and shoot everyone else. This plan put everyone at risk of getting shot and had no chance of success. But he wasn't thinking about the safety of anyone else, he was only thinking about what course of action made him feel better at that precise moment, with no thought for consequences. It was only luck that the truck crashed and he got knocked out long enough to not get everyone killed.
Later, when Kenny beats Carver to death. I do believe that killing Carver was justified. Tying him up for the walkers, putting a bullet in his head, or beheading him would all have been reasonable courses of action, depending on how much time you have and what resources you value. Taking out both his legs and savagely beating him to death, wasting precious time you don't have, wasn't a reasonable course of action. It doesn't matter that Carver hurt Kenny, indulging in violence like that put everyone else at risk.
How? First, he wasted two bullets, at a time when every bullet counts. Then he spent a good deal of time killing him, time he could have spent helping everyone else cover themselves in guts or dealing with Troy. He put his own pleasure ahead of the safety and survival of the group at a time when everyone should have been focused on getting out alive.
Then again when he continually berated and abused Arvo. Prisoners are a lot easier to handle when they don't fear for their safety. Aside from that, at that point they had to recognize that either Arvo would have to become a member of the group, or they were going to have to leave him to die. It was unlikely that anyone in the group was going to be callous enough to just leave a kid to die alone, so the focus should have been in trying to help Arvo come to terms with his situation. Let him grieve for his family and join theirs. Instead, Kenny took every opportunity he had to kick the kid around, alienating not only the kid himself, but everyone else in the group.
He was so blinded by his desire to hurt people, that he was completely oblivious to everyone else's safety. Including Clem's. Case in point: 
Regarding that scene, aside from the obvious, that he physically hurt her because he was too busy beating Arvo to keep track of what happened around him, Clem was freezing to death. Instead of helping to find wood or a way to build a fire, he decided to start hurting a kid that wasn't even responsible for what happened.
Many defend these outbursts as being willing to do what needed to be done, but the fact is that often, violence wasn't necessary, and had no purpose. Beating Arvo wasn't going to bring Luke back. It wasn't going to keep Clem warm. It wasn't going to keep AJ fed. All it served was to make him feel better about a situation he felt he had no control over.
Worse still, it's this consistently violent behavior, that no one else in the group condones or shares, that ultimately led to the group being split. Mike (and optionally Bonnie) choose to run away with the prisoner they've known for a day that stay around the violent person they've been around for weeks. Had Kenny reined in his violent behavior, no one would have had reason to leave, they wouldn't have freed Arvo, given him a gun, and got Clem shot.
The world is a dangerous place, and the way to protect people is to try and minimize the danger. Kenny never did this. Instead, he gave in to his impulses and made situations more dangerous. Always in the name of "protecting others", but that was just how he rationalized it. No matter how much he said he wanted to protect others, he was not effective at protecting others. He was like Ben and Nick, he had good intentions but a deep character flaw that prevented him from succeeding. Instead, everyone else had to do double the effort to work around his mess.
Of course, Kenny is a fictional character. It doesn't really matter how he behaves. What is disturbing, however, is how readily a lot of people here in the forums jump to defend these outbursts. Claiming that they would act the same way under those circumstances, and feel justified to do it.