I think that the main issue is on what grounds can any non-believer classify the world as 'evil'? Evil is just a relative concept, a subjective opinion like our taste in food. Likewise, humans are just animals and you do not call the lion evil for eating the gizelle or the monkey evil for raping the other monkey. By stating God cannot exist, or exists as an evil entity, implies that you believe in a real, objective law of good and evil, and wherever there is a law there is a lawgiver. Therefore, you believe in God. The odd thing is the fact that in order for a non-believer/atheist to use the problem of evil, they have to change the affects of their own worldview and borrow from the Christian worldview so that they have objective good and evil. Besides this, the obvious answer for why there is evil is because of free-will. God created man so that men might become like god writes St. Athanasius. And what is God's most distinguishable trait? His freedom of course. Therefore, humans, being created in His image with the purpose of becoming like Him through grace, also inherited free-will to an extent. Now, this free-will is something that we can use for both good and bad. We can use it to do what God wants, and thus bring peace and goodness, or, we can use it to do the opposite of what God wants, which, is sin and leads to evil and suffering. The biggest issue many people have is accepting the fact that in order to have free-will, we must have the freedom to disobey. If we did not have the freedom to disobey/do evil, then there would be no free-will because freedom by its definition includes both good and evil. And thus, if there was no free-will then there would be no potential for good, because goodness usually implies freedom, no one rewards someone for doing something unwillingly, even if it is great. And if goodness did not exist, then that would mean it is impossible for humans to become like God in the process we call Theosis. But, as a result of the Fall, it is true that mankind has horribly abused its freedom and has made things so difficult that it is impossible to come to God on our own, therefore, God came to us in the Incarnation and as a result of what Jesus has done, sin, evil and suffering, at least for the saved, has been conquered. As Christians, we no longer have to worry about the earthly suffering because God promises comfort at the end and eternal life, and, keep in mind that what I am going to say next is probably the most significant thing in this post. God has even redeemed pain by turning it into a way of redemption. As CS Lewis said 'God whispers to us in our pleasures, speaks in our conscience, but shouts in our pain; it is His megaphone to rouse a deaf world!' Because we have no more reason to worry about pain, God can now use pain as a way of strengthening us and revealing important spiritual truths to us that aid us in Theosis. And even when we make mistakes, God can use it as a way to correct us and show that we have done wrong. As for Heaven, Heaven is also going to be a place with free-will, but no one is going to abuse that free-will like they have done here. Because, in order to get into Heaven, one must really choose God before everything and meet all of His requirements. Do you really think God is going to accept someone whom He knows is going to rebel against Him into Heaven? No, the eternally damned will be cast into the frying pan because of their own free-will and the eternally blessed will get to come closer to God through eternity in Heaven.