Hatred, bitterness, revenge, loathing...it seems at the time like killing the person or making them feel the pain that you've gone through would make things better or make the person feel better. But it won't, because in the end, it will never bring the person who's died back. It won't heal the scars of how helpless you felt knowing you couldn't help them or save them from their fate. And on a personal note, it won't help heal the wounds if you had to see what happened in person.
It takes a special kind of person to take another's life like that, but it takes even more special and strong willed person to rise above it and try to cope and heal the emotional wounds--with time. Them dying, certainly, might make you feel better for a second knowing they're dead, but in the end, accomplishes absolutely nothing: you still have to cope with the pain.
I personally understand Katara's pain and anger but I'm glad she made the decision she did when she actually had the chance to kill the man. He was a pitiful, sad excuse of a person and it would have been too good for him. Though she shouldn't have said what she did to Sokka. That was way too hurtful, and for her not to apologize made me think less of her.