The most common refrain of atheists in explaining why they do not believe in God is the problem of suffering. The question runs like this: "How can there be a [good] God, with so much suffering in the world?" The question is rhetorical, because the questioner typically does not proceed to present the process by which they investigated this question and then concluded: there is no God. Few are polemicists. Those that do offer arguments will typically cite others, themselves polemicists, whose polemic will chiefly involve more lurid presentations of the question on the table: they cite parasites that burrow through the eye, cancer, the death of babies. These are no more than tabloid-isations of the question; they do not elaborate it or go any way to answering it.
There are indeed plenty of interesting arguments in this domain, but, as with any domain of value, it requires knowledge, attention, study, and patience. The domain is theodicy, and its tradition is long, learned, and worldwide. What appears to many to be a rhetorical question with only one acceptable standpoint is really the entrance point to a universe of philosophy and theology. Rather than walking through the door, which would require suspending one's own peremptory conclusion and returning oneself to a position of uncertainty (with its perils in both directions), the sign is flipped from 'open' to 'closed', and, along with it, the case.
I do not intend to present a treatise on the matter: merely to throw out a few obvious elaborations on the nature of the question, in the hope that a reader who has considered this case closed might, instead, consider reopening it.
First, I will expand the question: rather than just suffering, let's talk about both the features of the natural world that necessitate suffering and the feature of humanity that entails the possibility of evil: free will.
There are the causes: the material world and free will, with its attendant possibility and actuality of evil, and the consequence: suffering.
1. What is suffering? Suffering could be described, heuristically, as taking the forms of pain, uncertainty, practical impediment, conundrum, frustration of goals.
2. Why isolate suffering? Suffering is one small aspect of human experience. To take that one aspect and try to consider how a god or gods (or the one God) could exist, be good, and be omnipotent without considering all aspects of creation is folly. Would one examine the nature of a relationship, say, with a parent based on a cameo appearance, an incident, or even a recurring theme? Could a parent refusing to help a child with homework, refusing to comfort the child when its conduct has caused a friend to be beastly back, or more generally punishing or disciplining the child be considered without considering the totality of the relationship? Moreover, the isolation of suffering (one's own or proxy) automatically points the finger back at the individual, concerned not with character, morality, responsibility, growth, or achievement but comfort or freedom from hardship.
3. What would a life without suffering be like? A life without suffering would be a life without loss, without death, without difficulty, without risk, without challenge. Would you prefer to do crossword puzzles or find all crossword puzzles already filled in? Would there be any pleasure in playing the piano if you could sit down and play anything perfectly first time? Would life be better if you were so happy in a small room that it never occurred to you to leave it? Even cursory consideration reveals such a life to be insufferably dull and narrow. Note the word 'insufferably'. Human beings are designed to need suffering. The absence of suffering of any kind would be the source of the greatest suffering of all. The project of eliminating suffering cuts its own throat. The bloated, cosseted, perpetually supported, entitled, vain, and ultimately useless testify to this. Constructing their lives to avoid suffering and shift all responsibility to others they are the unhappiest of all. They invariably make themselves ill. The argument might be recast: maybe one could believe in God were there to be less suffering, or more evenly distributed suffering, or only 'fair' suffering, but any attempt to construct a world with tightly constrained suffering immediately becomes a ridiculously complex clockwork mechanism: the argument would then shift to trying to understand why God would permit this or that suffering. The question is granulated but not solved.
4. What would human life without free will be like? To abolish evil requires the abolition of free will. That, in turn, abolishes one's own. Is that really the desire? Or do we want only petty, manageable evil? How does one calibrate the acceptable quantum of evil? What sort of person would condone the presence of some evil but draw the line at the egregious? Is that not, itself, a form of evil, necessarily relativistic and subjective?
I will stop here. I hope the point has been made. The question, though it can be deployed rhetorically, has no merit as a rhetorical question. Even the most superficial attempt to begin an examination of this topic reveals the question to be far richer and far more revealing about the psychology of the questioner than is first apparent.