The most common objection to the existence of God is, “If there is a perfectly good, knowledgeable, and powerful God, why does evil exist? Either he is not all-knowing because he doesn’t know about the evil in the world, or he does know about it but is not powerful enough to stop it, or he is malevolent and does not desire to stop it.” So, it is argued, we are either left with a good God who is impotent to stop evil or an evil deity who could end all suffering and evil, but enjoys watching his creatures suffer. This is usually delivered in an emotionally-charged triumphalistic tone as if no possible solution could be given and therefore Christians should mind their own business and stop preaching repentance to those who enjoy their sins.
One thing to keep in mind about the problem of evil is that it is not a logical argument against God’s existence, but an emotional and psychological argument that is phrased as a logical one. That is, it is an inductive argument treated deductively. This throws a lot of Christians off because they are trying to answer the objection on the atheist’s own terms rather than by phrasing the problem as Scripture does. The Bible is sufficient to explain the origin and existence of evil in the world and what God is going to do about it.
The answer to the problem of evil is this: Christians believe that God has a morally just reason for allowing evil and suffering in the world and that one day he will do away with all evil and suffering at the Second Coming of Christ. Evil exists because sin exists, and until sin is done away with, evil will still exist until the time when Christ returns and conquers it. To do away with evil, God must deal with those who commit evil, and that’s all of us. The problem of evil begins with us and only those who trust in Christ will be spared God’s wrath. Without God’s wrath, those who do evil could not be punished.
The atheists are correct in asserting that a good God would do away with all evil and suffering. The problem is with demanding that he do so right now. Without the fall of man into sin, Christ could not have died since death only entered the world through sin, but the cross was God’s plan from all of eternity (Eph 3:11). God can even use evil and suffering to accomplish a greater purpose and the greatest example of this is in the murder of his own Son to bring salvation to those who believe (Acts 4:28). I would recommend Robert Morey’s book The New Atheism and The Erosion of Freedom and Randy Alcorn’s book If God Is Good for more information on how to answer the problem of evil.