The problem of evil can often be stated in many different ways but all amount to the same thing. Basically that there can’t be an all knowing, all powerful, good God if there is evil in the world because God would not allow or decree evil to be if He is all those things.
Without even getting into God’s purposes for creating the world. I say this, go back to the problem. The fact that there is a problem of evil to begin with, proves that there is no such thing as atheism. Because atheist do not believe there is a such thing as right and wrong. How could they? What would they have to base it on?
Greg Bahnsen in the Great Debate said this, "My answer to the problem of evil is this: there is no problem of evil in an atheist's universe because there is no evil in an atheist's universe. Since there is no God, there is no absolute moral standard, and nothing is wrong. The torture of little children is not wrong in an atheist's universe. It may be painful, but it is not wrong. It is morally wrong in a theistic universe, and therefore, there is a problem of evil of perhaps the psychological or emotional sort, but philosophically the answer to the problem of evil is you don't have an absolute standard of good by which to measure evil in an atheist's universe. You can only have that in a theistic universe, and therefore, the very posing of the problem presupposes my world view, rather than his own." (Bahnsen, in The Great Debate) If there is no God than non christians have no right to say that God is not good or God is not all powerful for not stopping evil in the world because if there is no God than whatever the non christian is talking about makes no sense whatsoever, because there is no evil. Atheism destroys itself at the reason level. The moment they start talking they have lost the argument because in there worldview there is no such thing as evil or good or anything absolute.
And so, though Christians often do wrong things, it is the Christian worldview that says it is wrong. And the atheist is borrowing from the Christian worldview when trying to point out all the bad things Christians do to argue against the Christian worldview.
In the atheist worldview there is no right or wrong, only opinion. So the problem of evil doesn't prove there isn't a God. It in fact proves there is a God. For without God there would be no way to prove anything. There would be no absolute standard. Including no absolute standard of which to base all morality on.
Without an absolute standard everything just boils down to opinion. Whether it is personal opinion, popular opinion, cultural opinion, or opinion on whatever brings about the most good. But nevertheless still opinion and that opinion could change depending on the person or persons or cultures or what have you.
And one of the biggest proofs, besides creation screaming out a million times over that there is a God is that our consciences tell us that there is a such thing as right and there is a such thing as wrong. Thus there is a God who declares such.
All people actually know this. It's just that many, many people are not consistent in their worldview and suppress the truth in unrighteousness. (Romans 1:18)
This is no new thing. All good philosophers know this. Without God, all things are permissible." The only consistent atheist is one who says there is no right or wrong. In order to get to that point, your conscience has to be really seared. But when you do get to that point it is why we have had people like Hitler who were so influenced by the idea of survival of the fittest. Because there is no right and wrong. Whoever is strongest is right and thus wins. It is why Neitzche could say, "do what thou wilt is the whole of the law". Meaning whatever you want to do is right because there is no right or wrong, only what you want and if you want it, that means it is right. Neitzche could say this because Neitzche also said that God was dead and Hitler loved this philosophy just fine because Neitzche also said there was a superior race of people called supermen. Sound familiar.
You say, yeah but Hitler twisted these ideas. Well I say, with no moral compass, how could you not twist these ideas. We have to have a standard. That standard can be us or it can be Him. When man is governing man, it is a bombshell. We have to be governed by our Creator, it is in our DNA, it is for our own good.
My friends, when we have lost Him, we have lost everything and there is no telling what can happen. God made us, God loves us, and He wants for His people to thrive but there is no thriving apart from Him. “The sum of your word is truth, and every one of your righteous rules endures forever.” (Psalm 119:160)