The problem can be stated in different ways but in the end it reduces to questioning God's reasons for providentially planning and sustaining the existence of evil. The question why does God allow evil and suffering in the world, I think is a difficult question. Here are some plausible answers:
Miscellaneous Videos Dealing with Evil from various Theological Traditions:
1. God has a morally sufficient reason for why he allows evil to exist. To argue he doesn't cannot be shown by limited human knowledge.
2. It is for a greater good. We do not see the big picture of all the events that occur but God is orchestrating them for ultimate good. For example, Jesus died by the hands of wicked men so those that repent and trust in Him may have everlasting life.
3. God created laws of nature. If God intervened every time evil or suffering occurred what would stop people from demanding God to intervene for everything at every time? It doesn't sound like atheists want evil and suffering to stop, it sounds like they want heaven on earth.
4. God uses evil and suffering to build our character.
5. God gave humans originally the freedom of choice. God did not force Adam and Eve to love and obey him. He gave them the ability to choose good or evil.
6. If God removed evil from the world, like rape, God to be fair would be obligated to punish not just some but all evil and suffering. Everyone would cease to exist because all evil and suffering is the results of sin. Everyone is guilty not innocent so all would cease to exist if God chose to destroy evil now instead of deal with it through the cross of Christ.
7. God created all things, rules all things, controls all things, and owns all things. This means God has the right to do whatever he wants with his property (i.e. creation). Or as Romans 9 puts it, the potter has power over the clay to do whatever he wills with it.
Ultimately I think it all comes down to what we put our trust in. Are we going to trust God’s infinite knowledge and wisdom or man’s limited knowledge?
Gregory E. Ganssle
The Free will Defense
What is Evil?
The Problem of Suffering and Evil. William Lane Craig (Part 1, 2 and 3)
JP Moreland Q&A
William Downing. The Problem of Evil. HERE
John Byl. God, Chance and Evil. HERE
Greg Bahnsen. The Problem of Evil. Covenant Media Foundation. HERE
Scott K. Oliphint. HERE
E. Calvin Beisner. The Potter’s Freedom. HERE
John Frame HERE
Greg Welty HERE
Cornelius Van Til HERE
Vincent Cheung HERE
Bruce Little. Evil and The God Who Knows HERE
William M. Schweitzer, Rethinking the 'Problem of Evil' in The Banner Of Truth Magazine, May 2013, Issue 596 (Banner Trust: Edinburgh, 2013)p.25.
Czapkay Suddeth, Michael. Absolute Predestination and Divine Permission.1989. p.p.66-75.
Paul Copan. "If God's Creation Was 'Very Good', How Could Evil Arise?"