As any apologist worth his/her salt will tell you, the great objection to the proposition that God exists is the fact of innocent suffering.
If you want a particularly vivid presentation of this complaint, go on YouTube and look up Stephen Fry’s disquisition on why he doesn’t believe in God. (Then right afterward, please, do look at my answer to Fry).
How can God allow suffering?
But the anguished question of an army of non-believers remains: how could an all-loving and all-powerful God possibly allow the horrific suffering endured by those who simply don’t deserve it? Say all you want, these critics hold, about God’s plan and good coming from evil, but the disproportion between evil and the benefits that might flow from it simply rules out the plausibility of religious faith.
The skilled and experienced apologist will also tell you that, in the face of this problem, there is no single, unequivocal “answer,” no clinching argument that will leave the doubter stunned into acquiescence. The best approach is to walk slowly around the issue, in the manner of the phenomenologists, illuminating now this aspect, now that.