You are assuming that feelings should have anything to do with this.
The problem I have with executions, besides the error-prone process that leads to them and the fact that I am not comfortable with the idea, is that it's a double standard; not because a society doesn't have the right to revoke one's life, but because it's borne out of the perceived need for revenge: someone hurt us, so someone will pay. We need to feel good about this situation again, and we still think that hurting or killing someone will do the trick. It's antiquated reasoning, and has no place in a modern society, where we know better than to think that it's a deterrent, or that it will actually make the victims or their loved ones feel better. The double standard is that we expect each other to act rationally, but we have laws which allow society as a whole to act out of rage. That's completely ridiculous, to me.