Many have asked why a good God would allow evil. Is God incapable of preventing evil from occuring? That is, is He not all powerful (omnipotent)? Is God not really all good? This is summed up in the question: “Why would a good and powerful God allow evil and suffering?
“The heart of the Free Will [Defense] is the claim that it is possible that God could not have created a universe containing moral good (or as much moral good as this one contains) without creating one containing moral evil.” (Alvin Plantinga, The Nature of Necessity (Oxford: Oxford University Press, 1974), 166-167).
God allows evil and suffering because they are a necessary condition of the best possible kind of world. Without sin and evil, there is no atonement. And without atonement, there is no incarnation. Thus, man’s fall into sin and evil is a “fortunate fall,” a necessary part of the best possible kind of world (Supralapsarianism, or ‘O Felix Culpa,’ in Christian Faith and the Problem of Evil, ed. Peter van Inwagen (Grand Rapids, MI: Eerdmans, 2004), 1–25.).
This is a difficult question to answer with brevity. A full treatment of the problem of evil can be found in the Ratio Christi blog.