I don't view execution as punishment or revenge. I view it the same way I view putting down a rabid animal. I would never take pleasure or vengeful satisfaction in it, even if the criminal had hurt me or someone I knew.
2. It's not significantly more ethical to keep someone that is innocent locked up in a prison for their entire life. Someone being freed after 50 years in prison has had their life stolen from them, even if they were not actually executed. The stakes for life imprisonment are just as high as execution. Arguably, the torture of prison makes it worse than execution in many cases.
3. Execution makes sense in some rare cases, where the criminal is very clearly guilty (e.g. video evidence of them murdering multiple people) but only as a way to prevent them from hurting people in the future. Not as a deterrent, punishment, and not for revenge.
4. If I was a sociopath serial killer that couldn't help myself, I might view execution as a relief. Even if outwardly I was begging not to be executed, I might appreciate that my society had the courage to kill me instead of leaving me to rot in prison for 50 years.
5. Ultimately, we need to be able to cure these people and release them back into society. Science just isn't there yet, so for now we have execution and life imprisonment as our primary tools. No one should be satisfied with either option. They're both terrible options that are not as dissimilar as some portray them to be.