So the idea of an eye for an eye leads us to some pretty startling conclusions if we apply it rigourously.
Let's say one person murders another in cold blood, it seems straight forwards. What if its an accident though, a car crash for example, ok perhaps it's one person's fault, but it wasn't intentional, right?
So what about if someone parks their car in the entrance to the hospital emergency wing, and ambulances can't get in and several people die due to the delay. The selfish person who parked there should have conceived that that harm might occur, but they did it anyway, should they give their life?
Just how far do we go, do two deaths create a balance, or does it just cause pain to more innocent people? That second part is what it's all about, what if someone I love causes that death, and is killed by the state, what am I supposed to do with that grief? I'm suffering, what for? What if later the was a miscarriage of justice; can I have the judge, jury or lawyers executed?

The death penalty does nothing to deter true murderers (or there would be none) and causes undue suffering to innocents.