The “problem of evil” is famous. If you believe in a God who is all-powerful and sovereign over the world and together is impeccably good and just, then the presence of evil and suffering creates a problem. This timeless report of it was provided by David Hume, in his Dialogues Concerning Natural Religion. “Epicurus’s old questions are yet unanswered. Is he willing to prevent evil, but not able? Then he is impotent. Is he able to but not willing? Then he is malevolent. Is he both able and willing? Whence then is evil?”
The problem of evil is commonly contemplated now and certainly causes a real question to believe in God. Some God who is all-powerful and all-good would likely prevent terrible evil and suffering because he would have the ideal capacity to do so. But evil does happen and continues to happen. Consequently, this all-powerful and loving God either cannot be or probably does not exist.
At this point, I’m assuming you the reader are a Christian. However, to quickly address how I would handle a non-believer, I would employ a form of the moral argument. Because without an absolute moral standard, which requires an absolute moral standard giver (God), the non-believer has no grounds for a true complaint against evil. Former atheist C.S. Lewis summarizes how this thinking eventually guided him to Christianity: “my argument against God was that the universe seemed so cruel and unjust. But how had I got this idea of just and unjust? A man does not call a line crooked unless he has some idea of a straight line. What was I comparing this universe with when I called it unjust?”
Considering again, that you are probably a Christian, I want to first communicate evil is a privation. Then, I will follow with the best of all possible worlds theodicy, which will naturally lead to the free will defense and the greater good principle.
I want to make sure you are not going to assume evil is a “thing” that exists, and God is the cause. Both Augustine and Thomas Aquinas point out that evil is not a real entity in the world. This does not mean evil is illusive or imaginary (as the Christian Scientists and Buddhists tell), but evil is not a material or a phenomenon that exists by itself. Evil describes a deficiency or denial of good. This deficiency is known as privation. A congenital anomaly or an infection is a lack of good well-being. A sin, like assault or homicide, is a lack of the proper love shown to another person. Just as there is no actual equal inverse being to God, there is additionally no actual equal inverse thing to good. Evil is what occurs once the good is altered or distorted. Remember in Genesis 1-2, God told us all that existed was good. Evil was not an innovation, but a distortion. God is not the writer of evil, but a permitter of it.
 David Hume, Dialogues Concerning Natural Religion, ed. Richard Popkin (Hackett Pub, 1980), 63.
 C.S. Lewis, Mere Christianity (New York: Macmillan, 1952), 19.