This is among the most difficult questions to answer, and I don’t have any particularly innovative solution to offer that hasn’t already been proposed before. A short listing of the most notable answers can be found here. They provide some food for thought, and may help explain why a world with some suffering in it could be preferable to a world with none at all. For a vivid illustration of this, I’d recommend the Twilight Zone episode A Nice Place to Visit.
Nonetheless, I would agree that if God is good, the quantity and intensity of suffering we observe in this world are much higher than one would expect to find. It does seem to me that free will, potential for love and moral growth, challenges and lack of boredom, etc., could all continue to flourish in a world with, say, only 5% as much suffering as the one we live in. So I will concede that I have no answer to this question that anyone will find completely satisfying.
However, the problem of evil is not an argument specifically against Christianity, because the same question is just as baffling if it is phrased in other ways. For example, “if there is no God, why is there so much suffering in the world?” is perhaps even more difficult to answer. Why would suffering exist at all in a world without souls? And where do souls come from at all, in a system of thought where nothing but physics governs the universe and man is essentially just a biochemical machine? If man were nothing more than his evolutionary biological nature, one might expect some level of evil (driven by competition for food, etc.) and some level of good (maternal instincts, etc.), but not the extremes of both altruism and cruelty that we see, and certainly no concept of us consciously “experiencing” anything. Atheists have their arguments to explain how things might have evolved to be this way, but they are even more unsatisfying than the Christian ones. Furthermore, to be philosophically consistent, atheists usually have to deny that good or evil or morality are anything real or objective, just pre-programmed instincts. This position forfeits their right to be morally outraged towards a Christian’s description of God, or anyone’s suffering.
If neither atheism, nor Christianity, nor any other religion that describes God as good is true, there are in principle other options. Some sort of partially-good God, or a multitude of Gods, or two equally powerful Gods, one good and one evil. Such a description of reality might be less vulnerable to the problem of evil, and people believe in things like that at various times and places. But any such system would be hard-pressed to say where we got our standard of good to begin with, if not from God. If God is not the ultimate good, then what or who is He subject to? By what power or truth can God be judged? Furthermore, I know of no serious and comprehensive attempts to argue for the existence of a God who is not good, at least not in the same way and with the same rigor that Christians and atheists argue for their systems. If anyone genuinely believes in such a thing, I’d be interested in hearing why.
There is, however, the potential to accommodate the idea of opposing powers within a Christian worldview. Specifically, we can say that God is good and Satan is evil, and they are struggling for the souls of the world. Much of the evil in nature or in men’s hearts might be ascribed to Satan rather than (directly) to God. This doesn’t negate the problem of evil, because Christianity claims that God ultimately created and governs everything. So, whatever evil Satan does is (indirectly) God’s fault as well, just as the problem of evil holds God responsible for the existence of evil men. However, while the problem of evil is not “solved” by this line of thinking, it does call into question our ability to judge the quantity of suffering as being more than is necessary to accomplish God’s purposes, because we don’t see the whole picture. There is probably a drama going on between God and Satan, angels and demons, that we have no knowledge of. Christ doesn’t give us many details about who Satan is, or why he rebelled against God, but He did say that Satan exists and has our worst interests at heart, and that we need to be on guard. Perhaps that’s all we need to know, or are capable of understanding, for the time being. This seems to me to be essentially the message of the Book of Job as well.
The world is what it is, and we have to fit our theory of God around the facts, rather than insist that God fit our idea of what the world should be like. As a 3-year-old getting my hair washed in the sink, I once really believed (on some level) that my mom was actually trying to drown me. I didn’t understand how such a painful thing could be possibly for my own good (now, I don’t understand why washing my hair was so bad, but I vividly recall feeling that way at the time). Still, on another level, I nonetheless trusted deep down that she did love me and was doing what she thought was right. Perhaps that is analogous to us trying to judge God’s motives (or existence) based on whether we find the world suitable to our standards.
To summarize, if Christianity seems unable to explain suffering to us in a satisfying way, it should be noted that no other system can either, and it should be kept in mind that there are good reasons to believe in God generally and Christ specifically on other grounds. What Christianity does offer is a message of hope, in four things. First, God Himself suffered too; whatever His ultimate reasons for allowing it, He was willing to take His own medicine. Second, those who knew God most intimately suffered too – the faith of the apostles was not born of an easy life but of the amazing things they saw and the confidence it gave them. Third, God is not indifferent to our pain. He weeps with us. Fourth, God promises a future with a new heaven and a new earth, where every tear will be wiped away.