I have two major oppositions to capital punishment, and neither are rooted in the possibility of rehabilitation or not.
The state is not infallible. If you put someone into prison for ten years and find out you messed up, you can at least release them. You can’t give them those years back, but you can try to do right by them as much as you are able. You execute the wrong person? You’re just a murderer.
Personally, life in prison (and not a cushy wall street exec prison) seems like a way worse punishment. Even if I was only concerned with providing somebody the worst possible punishment, lifetime imprisonment would be worse.