Atheistic apologists are expert manipulators, and one of their most effective strategies is emotional arguments. It is a major flaw of human nature that we tend to act on our emotions, rather than clear and reasoned thought, meaning it's easy to manipulate people if you know how to tug at their heartstrings.
To really illustrate this point, consider the fact that one day, we're all going to die. Already, you are aware of the fact that you do not want to consider your inevitable demise. It's a fact, but it's not one we generally want to acknowledge. Even when we do talk about it, we often use euphemisms, like "passed away". This is an example of emotion taking over reason.
Far greater, then, is the issue of child rape. The very word "rape" is soul-splittingly awful. Combine it with "child", and suddenly, even my muscles tense up as I type it. It's easy to see, then, how it might be a convincing case for atheism to point out that God has the physical power to stop every possible instance in which this terrible crime might occur, and yet, He does not. It's the problem of evil times 10,000! But as emotionally difficult as it is, there is a rational answer.
First, we can turn the tables on atheism. To illustrate this, let me first ask you a question: Is the recreational use of cannabis illegal? Here in the UK, the answer is yes. You cannot legally grow, sell, distribute, or even possess cannabis in the UK. It is a class B drug, the possession of which can bring an offender 5 years in prison, and an unlimited fine. But in some states in America, such as California or Colorado, the recreational use of cannabis is entirely legal.
But what about on the moon? The moon, of course, is not under the jurisdiction of any country. There are complicated legal theories about prosecuting crimes committed outside of one's own country, but ultimately, since there is no government on the moon, there are also no laws. Legislation requires a legislator. You cannot call something "illegal" if no such legislator exists. What that ultimately means is if there is no God, there is no sin in child rape.
As a Christian, I believe there is one God who is sovereign over all things. His "thou shalt nots" are universal. If something is evil in the UK, it is evil in California, in Colorado, on the moon, you could fly beyond the bounds of the furthest celestial body, sin is sin. Therefore, I can, and indeed must condemn child rape. I must also condemn other sins. Murder, theft, adultery, parental dishonor, blasphemy, things like that. We'll get to that, but for now, consider that if there is no God, all of that becomes relative.
In other words, in reality, an atheist may accurately assess that child rape is wrong, but their philosophy cannot sustain it. If there is no God, all things are equal and permissible. So, first, if you absolutely must think with your feelings, which is the better statement:
A. Child rape is absolutely evil, no one should do it, anyone who can stop it should, but tragically, evil people will do it anyway.
B. Child rape is morally equal to childbirth. I don't personally like it, I would stop it if I could, but some people will do it, and their opinion that it's ok is morally equal to my opinion that it isn't.
The obvious answer is statement A. Yet, this is the Christian answer. So, yes, you do have the tragic fact that child rape does happen, and it's hard to understand why a truly good God would not use His omnipotence to stop it, but this is still significantly better than to say it's morally permissible, but most people find it distasteful.
Nevertheless, we are still left with the question of why God allows this, and other heinous crimes, to occur. Why do we see rape, terrorism, tyranny, kidnapping, slavery etc. in the world? And if good human beings, including Christians, are willing to step in to fight them, why doesn't God do the same?
To answer that, let's ask another question: How much evil should God stop? Most people will say "all of it", and that's actually correct. And a time is coming when God will do exactly that. Everything will be made new, and every thought, word, and deed, will be accounted for. Child rape will be permanently abolished, never again to even come to mind. But what about "smaller" evils? What about the times we use God's name in vain? What about the times we cuss out someone we don't like? What about all that porn we watch? What about the extra-marital sex we have? The blasphemies we utter, the small thefts we commit, the "white" lies we tell, the euphemisms we use to downplay our sins, these are all evil things, deserving of God's wrath.
Imagine a world in which the bigger evils were taken care of. Heck, you don't need to; others have done that for us. Look at a kid's show. So innocent to us. As adults, we know true evil. We see the chaos and bloodshed in our world. But the children to whom these shows are directed, hopefully, do not. We're supposed to shield them, and so if a character so much as says a rude word in a show, it gets a higher "rating". Thus, when kids do see these things, it's a whole new world of evil to them.
From this, we can reasonably assume that if God erased the worst of evil from this world, all that would happen is we would still complain that He hasn't done so. It's just that we would instead be saying "if I could stop someone from stealing $20, I would. That is the difference between me and your God."
Thus, this snappy atheist slogan actually backfires, as it shows the real difference between God and the atheist. Whereas the atheist only sees, and wants to stop, the worst of evil, he is quite blind to his own sin, which he has no desire to stop even himself from committing. He's quite content for God to let him watch porn uninterrupted. He'll call you a bigot if you tell him homosexuality is a sin. He'll cuss you out all the more if you politely request he watch his language. There will be no end to his blasphemies until the day he either repents, or meets God face to face. The difference between God and an atheist isn't who cares about evil, but who cares most about evil.
But there is another difference between God and man. Even as a Christian, there are limits to my love and mercy. If I ever had a son, and that son turned into a rapist, I would feel no remorse for delivering him over to the consequences. Even if that meant I had to kill him myself, that would be on his own head. But beyond all imagination, God took the consequences for sin on His own head.
Time and time again, the Bible tells us God takes no pleasure in the death of the wicked. Not that He is unwilling to kill if necessary, but it brings Him no joy. What really pleases God is when the sinner repents. Thus, Jesus, being completely sinless, was crucified, suffering the full wrath of God for sin. All who believe in Him may therefore receive salvation, whether they are as innocent as Robbie Rotten, or as vile as the devil himself. Because of God's unfathomable mercy, when He destroys all evil, you can live out eternity as a perfected, new creation.