The single most damning indictment against a deity establishing or allowing a strict dichotomy of eternal reward or eternal punishment is the inability of such deity to ameliorate such condition once it has been imposed. But some theistic accounts propose just such a dichotomy, specifically outlining categories of finite conduct which lead to infinite punishment -- even for those who would not naturally be aware that such conduct is condemnable.
Theists typically seek to sidestep the issue by proposing that human beings, having free will, are given the ability to choose to be so evil that forgiveness is not deserved. But once the punishment exceeds the wrong, unforgivingness itself becomes purely vile evil. At that point the finite wrong has already been punished, and the once-wrongdoer is being punished for nothing. A being would therefore itself need to be an infinitely evil scourge on the face of existence to permit an infinite punishment for a finite wrong. Naturally, it is a compoundedly greater error to make a binary inquiry of this, addressing only the punishment of the most evil humans. In fact, some faiths suggest a deity so basely evil that it would impose an eternal punishment on somebody who simply never came to believe in the existence of the deity in question despite living an otherwise good, even flawless life (and, perhaps, even if this disbelief is a logical response to incompetent evangelism).
Islam (so far as I am given to understand) avoids this fatal error by providing that the 'sinner' retains the ability to repent and obtain forgiveness even after death, i.e. even while in Islamic hell. Which is a more sensible thing, after all, since the infinite impossibility of such a thing would require a most sadistic elimination of free will. Simply put, if our minds continue to exist after death at all then we retain the capability to change our minds. If we can not change our minds, if we can not repent our wrongs, then the minds being punished are not truly our minds; they are no more than constructs of a static version of our minds, created for the sole purpose of having torment imposed upon them (if we ever actually existed in the first place). Conversely, if our minds (and their defining free will) are able to continue, then we are able to change our minds, and all must be able to go from a hell to a heaven or from a heaven to a hell based upon their change of mind. In other words, it can not be the case that the consequence is both infinite, and unfixable for the duration of that infinite period, for that would eliminate the free will from which the situation is claimed to arise in the first place, eliminating any justification for punishment.
Ultimately, the simple mathematical impossibility of a finite mind being fully aware of an infinite consequence is what makes infinite consequences inherently evil as applied to finite actors. The human inability to truly understand infinites is exemplified by the fact that we are only able to discuss the infinite through the use of finite symbols and representations. But of the entire set of "condemned" souls, there must be one which is, of that set, the least deserving of condemnation -- so the question remains, why does the least deserving condemned person remain condemned? And why would this condemnation persist even when the condemned person least deserving of condemnation had been fully punished or had fully repented after, say, one hundred billion years of torment? Why not, when the least deserving saved person is saved for all time, even if they become no more worthy of it after salvation, or are even able to slip into thoughts meriting condemnation?