Why does evil exist?
Atheist point to evil as proof that God does not exist, because a loving God would not let bad things happen to good people. But if you believe evil exist, good must also exist. If good and evil exist then there must be a moral law by which to distinguish the two. If there is a moral code there must be a moral law giver, in other words God.
We went from how can God exist if evil exist, let's go to "How can evil exist if God exists?" If God is the moral law giver than he exhibits the ultimate ethic, which is love. Love then necessitates freedom. He gives us the right to choose. He tells us what is good for us, but we can choose to ignore it, and bad things happen.