I comment on a fine speech by John Lennox at Pepperdine University in 2013:
Epicurus starts with the 'god of the philosophers' not the creator God of the Bible. As do most who enter this type of discussion. So we ask the wrong question, we misunderstand the Creator God and we under-estimate ourselves. We prefer to think of God as the puppet-master fairy god mother god and we as the poor waifs that he will wipe the nose of.
The first thing people do in questioning evil is to distance themselves from it: we fail as people to recognize that however 'good' we think we or others are, we are full of evil: selfishness, pride, and disdain for others. We match the 'evil' of this corrupt world perfectly as the corruption is the outcome of Adam's rejection of 'god-ward-ness' We continue on the path Adam identified. Thus Paul in Romans 8:18ff (compare Psalm 115:16).
This is so because we are in God's image (Genesis 1:26: ponder on it) and our words and actions have real meaning; but without 'god-ward-ness' our words and actions are corrupt and as the stewards of the creation, our corruption drags it down as God, like Elvis, has 'left the room'. Yet he stays to seek our good by our repentance; our rejection of 'not-god-ness'.
So, the world is a broken place, given over to futility and corruption. Why?
1. Because we could not 'fit' as corrupt people if the cosmos was uncorrupted: the would be an unbridgeable existential rift that would make life impossible.
2. That we have enough of God's imageness to understand that the world is broken and we can detect that it ain't right, even though we are part of the not-right-ness.
The benefit of this is that our being out of synch with the God of life (Jesus: the way, truth and life) who is love, rubs us up the wrong way at every turn. We are reminded of the disjunct in everything we do, think and hope. We all face death all the time: it looms at our end. Thus, when Jesus was asked about the Siloam construction accident (Luke 13:4) he said: repent, lest this also happen to you (that is, die without repenting?). That's how we deal with 'the problem of evil', repent! Turn to Christ for new life.
Now, that's how the Bible leads us to think about evil: we experience it because our 'mannishness' is 'god-like', and that is the constant alarm siren that things are not as they should be. But pastorally, we don't handle it this way: we share the other's grief, we listen kindly, we be with them, we give any practical support and succor we can. We show our love by our actions and seek to bring peace to them.
Here's my addendum, a comment to a question to Frank Turek:
God can't just forgive all sinners? He has, but its up to sinners to take up the forgiveness by repenting of their rejection of God and so rejoin his family. God does not impose himself on sinners (God is not a Calvinist!).
Its about life transformation, and doesn't work with people who want to remain in rejection of God. Too much moralism which characterizes much of US evangelicalism. It under-does the gospel and misleads people. Sin is at base our willful alienation from God: it is us saying "no, God, get gone" The gospel is about being in fellowship with God and having new life in Christ to enable this.
And it is something we must come to realize: that we are cut off from such by our corruption in a corrupt world. The scheme of Salvation is about fellowship, God over-restoring the world if Genesis 3:8a where he was in fellowship with Adam and Eve. The 'over-restoring' is the new creation, with this veil of tears 'rolled up' and superseded.