I kill a lot of rats for work (I'm not an exterminator; I'm a scientist!). "A lot" is, of course, a relative term, but suffice it to say that I've killed hundreds of rats with my own hands. Every time I have to feel the flesh being cut, and the bone breaking. It doesn't make me want to vomit anymore, but it took quite a long time to get used to. I think civilized people should have an aversion to killing. I also think that doing it at a distance (such as sticking a needle in an arm then pressing a button; or, as in your example, buying meat off a grocery store shelf) completely removes the gut-wrenching side of killing, which is really where it's humanity lay. It's east to pretend that the delicious ribeye on your plate has nothing whatever to do with a bolt to the brain of a once living steer. I'm guilty of that all the time. We are certainly willfully unconscious of it as a society. The way we kill prisoners is emblematic of a huge problem.
I know the feeling. One of my jobs at a restaurant included emptying the mouse/rat traps. I don't know why the boss wanted to use humane traps, since we were in an area where we couldn't really let them go. Lucky me! I think what bothers me about how prisoners are executed, is as you pointed out, that people don't want to take responsibility for the action. Thus the traditional executioner's hood. I admit that there are some people who cause such great harm to their fellows and the society they live in, that execution will be a viable solution. I don't think that lifetime imprisonment is a humane practice and I think that at this point, correctional practices and techniques can only be so effective and only for willing participants. That said, I do think that we all should take responsibility for the killing of prisoners, but diffusion of responsibility is very real. If there were some way to impress the personal responsibility and burden of killing on each individual who benefits from it, as well as support structures in place to help people understand and deal with those feelings and experiences in a constructive way, I think that we might all be better for it. But, that's still firmly in the realm of science fiction, as far as I know.It doesn't make me want to vomit anymore, but it took quite a long time to get used to.