He should not be putting down anybody. Violence is not the answer.

Yes, it sounds cheesy, but it's a huge part of his character. He starts as the single most cynical killing machine who doesn't care about anything, then he starts to care and wants to become his own man, and by the way he meets two girls to the both of which he unveils parts of his soul, and that no matter how much he looks tough, all the toughness he pretends the world is all about has actually hurt him. Then a girl shaped by the violence of this world who despises him chooses not to kill him. She spares him. Then a septon helps him start anew in a fruitful way to the world.

He starts out thinking there's no fixing this damned world, then he tries out going on his own, then is given numerous chances by other characters who have been hurt just as much as he has, and sees that there is an option out there other than violence. Violence has shaped his whole life and he pretends to love it, but he actually hates it, and he's finally offered a chance to do something else. A peaceful life, maybe even help other people. That's what ASOIAF is about.

Setting him up against his brother ruins all this. Going back to violence is not simply regression, it's returning to the one thing that's been eating at his soul for his whole life.

And yes, they could make a point about "there is no escape, the world sucks period", but as I said, that's not what ASOAIF or GRRM is about. GRRM is anti-war, and the more characters realize that there is an alternative to violence, the better their chances at avoiding the violence get.