Video from Closer to Truth
"The problem of evil troubles believers and well it should. How to explain the moral evil of human acts and the natural evil of nature? How could God be both all-powerful and all-good? Philosophers of religion offer 'defenses' (no logical contradiction between evil and God's existence) and 'theodicies' (complete systems explaining why God allows evil). But do they work?" video introduction
“The problem of evil” includes the phenomenon of evil ( pain and suffering) as evidence against the existence of God. For a great many people, this evidence appears decisive, because if God existed, he would be powerful or wise enough to prevent such evil, and good enough to want to prevent such evil. Since there is evil, therefore no such powerful and good being exists.
Christians have typically proposed two points in response: theodicy and inscrutability. First, God may very well have a good reason for allowing the evil he does allow (compatible with his holy and good character). Theodicy goes on to explain in more detail many of these reasons. Then the fact that unbelievers may not be able to discern or correctly guess at God’s justifying reason for allowing evil is not good reason to think he doesn’t have a reason. Given the infinity of God’s omniscience, complexity of his providence, and our own substantial cognitive limitations, we shouldn’t expect to guess God’s reasons.