Replying to Death Penalty?

So, Kenny Richey is a British dude who's been sitting on death row for 18 years. His conviction was overturned by an appeals court earlier this year which has just been over-ruled by the Supreme Court. I don't know many of the facts but it appears that in 1986 he started a fire in his girlfriends apartment to get revenge on her for cheating on him or something. Tragically this arsehole killed a little 2 year old girl, she would be the same age as me now if she was still alive.

Now, I'm not condoning what this guy did, he killed someone and deserved to be punished, but is it really right to execute him for it? Is it right to execute anybody for that matter? I can't claim to know a huge amount about the death penalty in the US but I find it hard to believe that the majority of American people still believe that it is the best way to deal with criminals. What justifications are there for still using the death penalty?