Why does a good God allow evil to exist?

If He is powerful enough to stop wrongdoing, then He Himself must be an evil God since He’s not doing anything about it even though He has the capability. 

Is He a bad God or a God that’s not all powerful?

One of the most haunting questions we face concerns the problem of evil. Why is there evil in the world if there is a God? Why isn’t He doing something about it? Many assume that the existence of evil disproves the existence of God.

Sometimes the problem of evil is put to the Christian in the form of a complex question, “If God is good, then He must not be powerful enough to deal with all the evil and injustice in the world since it is still going on.” Even the biblical writers complained about pain and evil. “Evils have encompassed me without number” (Psalm 40:12, RSV). “Why is my pain unceasing, my wound incurable, refusing to be healed?” (Jeremiah 15:18, RSV). “The whole creation has been groaning in travail together until now” (Romans 8:22, RSV). Thus we readily admit that evil is a problem and we also admit that if God created the world the way it is today, He would not be a God of love, but rather an evil God.
However the Scriptures make it plain that God did not create the world in the state in which it is now, but evil came as a result of the selfishness of man. The Bible says that God is a God of love and He desired to create a person and eventually a race that would love Him. But genuine love cannot exist unless freely given through free choice and will, and thus man was given the choice to accept God’s love or to reject it. This choice made the possibility of evil become very real. When Adam and Eve disobeyed God, they did not choose something God created, but, by. their choice, they brought evil into the world. God is neither evil nor did He create evil. Man brought evil upon himself by selfishly choosing his own way apart from God’s way.