John L. Mackie's inconsistent triangle:
1) God is omnipotent
2) God is omnibenevolent
3) Evil exists
Mackie points out that it is logically inconsistent for all three of these statements to exist simultaneously.
An alternative solution to the inconsistent triad is to remove one of the statements. However, if we remove the characteristic of omnipotence from God, then we can understand why evil exists, God does not have the power to defeat it. However, this does not satisfy religious believers who believe omnipotence is in God's nature.
By removing the characteristic of omnibenevolence then there would be no reason for God to remove evil from the universe as he wouldn't care for his creation. However, this unloving God is far from the perception of the God of classical theism.
Finally, we can remove "evil exists" as there would be no contradiction for God's nature, however, through observation we can see that evil exists in the world. This could be argued against by saying that our humanly perception of evil is warped and we cannot be sure of our moral values.