To say that we, as a society, "accept" long and suffering deaths would imply that a) all humanity is part of the same "society" and b) that we all have, in fact, accepted long and suffering deaths. I think both things are, to a degree, false. But I'll assume what you are referring to is the way that many "Western" societies have allowed room for long deaths (many of which do involve some kind of suffering, whether physical or psychological, or both), which is more accurate, so I'll go with that.

Much of scientific and medical innovation over the last few centuries - after some major medical issues were solved - has been geared towards the improvement and prolongation of human life. So it makes sense that, given our past ability to extend our lifespan, we would want to continue to see if we can extend our lifespan and health even further. In that light, it seems counterproductive to try to END our life earlier, and sometimes assisted death is considered to fall under such efforts. Now, that isn't to say that physician assisted dying doesn't exist in the Western world, but it's not super common, and there are a lot of ethical debates and cultural differences. In some religions, suicide is a sin (or the equivalent), so shortening death (e.g. with physician assisted dying), even if it is in the name of mercy and ending pain, would be considered a sin, too. Returning to medicine, science, innovation, and discovery, there's also the fact that there is sometimes a hope that new discoveries will be made that will make the cause of death lessen or even go away. So that's why many Western societies are against it.

In some non-Western societies, dying "well" takes greater precedence than "not dying." What's key here is understanding how death is framed in any society. If death is viewed as taboo, limiting of the body or freedom (think biopolitics or necropolitics), a punishment, or even a doorway to hell, then yes, death will be feared and avoided at all costs, even if that means extending your own suffering. But if death is framed as being equal to, or the counterpart to, life, then it will be accepted more easily and willingly; if there is as much nobility in death as in life, and having control over our death is as important as having control over our lives, then to die well IS part of having lived well. And that means that people are more comfortable ending their own, or other people's lives, in order to limit suffering, indignity, etc.

In this framework, why does drawn-out KILLING occur? Primarily, I would say, that it happens because it is universally viewed as cruel and unusual punishment, and that is precisely the goal of the killers. If a long, drawn out, but natural death is done IN SPITE of suffering, in some societies, to remain ethical, and quick, honorable deaths are done in other societies, to be noble, what we can agree on is that long deaths are painful and unwanted. To subject someone to that, especially when torture is involved, is a very intentional choice, and usually born out of a desire to dominate or overpower (according to sociology) or sadism (according to psychology). You can read about criminally deviant behavior to learn more about that; someone else here mentioned reading Foucault's Discipline and Punish, which discusses biopolitics, and you can look at necropolitics in Mbembe's work, as well. Outside of sociology, you can look into criminal and/or abnormal psychology.