Let’s take Naturalism to be the thesis that God, or anything at all like him, doesn’t exist. There’s no God, there’s no demons or ghosts. Nature is all there is. Some atheists contend that Naturalism is a good explanation for suffering and evil. They claim it explains atrocities like child molestation, rape, and the Holocaust. Let’s take a further look at Naturalism, Evolution, and explaining Evil.
In a recent exchange on the topic, it was argued that Naturalism explains a wide range of data. When pressed on this, the atheists punted to evolution: Evolution leads us to expect humans to act in ways that further reproduction and survival, not necessarily ways that promote moral behavior. Here’s what is meant by Evolution:
The atheists above weren’t saying that Naturalism explains the data, but rather that Naturalism & Evolution explains the data. Evolution to the rescue! Here are 3 reasons Evolution is not Naturalism’s savior.
1. Naturalism doesn’t predict Evolution.
First, nothing about Naturalism (so defined) actually predicts Evolution. Naturalism is perfectly consistent with Evolution being false. Why is this a bad thing? Well, if this is true, Naturalism suffers from what Robin Collins calls probabilistic tension:
In our case, Naturalism represents h. If h is really the conjunction of Naturalism & Evolution, then we can represent Naturalism as h1 and Evolution as h2. Since the probability of Evolution on Naturalism is very, very low , the probability of h2 given h1 is very, very low. Following Collins, this leads us to conclude that the prior probability of h is extremely low.
This conclusion is highly significant. Atheists do not usually say that the prior probability of Naturalism is low. In fact, some think it much higher than Theism (see Draper). Another key point here is that a low prior could negatively outweigh any confirmation that evil and suffering gives Naturalism. So even if Naturalism explains the data of evil and suffering apart from Evolution (of which I am dubious), Theism could still have a much higher posterior probability.
2. Don’t we just know it?
Suppose the Naturalist sees this problem and decides to reorganize their equation. Instead of adding Evolution to Naturalism as a theory, they decide to add Evolution to our background information (in other words, they’ll say Evolution is common knowledge to everyone; it’s something we all know to be true). Voila! Problem solved. Right? Wrong.
If Evolution is part of the knowledge we bring with us, then every hypothesis explains the data. Why is that? Recall that Evolution was originally introduced in order to explain evil and suffering. Since Naturalism can’t explain anything, it’s actually evolutionary pressures (like reproduction and survival) that explain the data. However, if Evolution is common knowledge, if it’s true regardless of the theory we’re testing, then the data of evil and suffering is expected on every hypothesis (since evolution is in the background). But if the data is equally explained on every hypothesis, there’s no way evil and suffering can be evidence for Naturalism over Theism.
Also important: adding Evolution to the background knowledge doesn’t do away with the probabilistic tension mentioned above. So even if this point fails, the tension remains. 
3. Why not add Evolution to Theism?
The third problem is that, if the Naturalist can add evolutionary theory to Naturalism, why can’t the Theist do the same? Responding by saying, “God probably wouldn’t use Evolution,” won’t work. Even if Evolution is unlikely on Theism (e.g.: God didn’t have to use Evolution), the same is true for Naturalism. Even in the small subset of Naturalistic worlds that contain biological life, Evolution wasn’t needed to bring it about.  Thus, if the Naturalist can make use of Evolution, why can’t the Theist? To suggest otherwise would be a clear case of special pleading.
Essentially what’s going on here is that the Naturalist is giving a coherent Naturalistic story that explains evil and suffering. I’m saying the Christian can do the same thing, using the same theory. Evolution and Christianity are compatible in the same way that Evolution and Naturalism are compatible. 
A Final Consideration 
The Naturalist might think what’s going on in the first and third point is that the Theist is trading the fine-tuning argument in for the problem of evil. Evolution is unlikely on Theism because of the problem of evolutionary evils, and evolution is unlikely on Naturalism because of the problem of fine-tuning. The idea is that these low probabilities cancel each other out. Here’s the rub: evolution is unlikely for different reasons. There’s an asymmetry between the two hypotheses. So the naturalist could retort by saying something like, “Fine-tuning aside, Naturalism is still superior in explaining evolutionary evils.”
This objection requires two things: (i) setting fine-tuning aside, and (ii) establishing that the probability of Evolution given Naturalism is higher than the probability of Evolution given Theism. Regarding (i), we can set fine-tuning aside for the sake of argument, but that isn’t something we can do in the end, ceteris paribus. In other words, the Naturalist can’t defend (ii) by assuming the failure of fine-tuning. In any case, let’s set it aside. A defense of (ii) requires calculating two variables:
(2) The Probability of Evolution given Theism
Only after having answers to (1) and (2) can we say that (ii) is true. So, what are the answers? These are questions the Naturalist must answer. (Importantly, a high probability for (2) has been defended here and here.)
Since Naturalism can’t explain anything, some atheologians feel forced to introduce evolutionary theory into their arguments from evil. This creates probabilistic tension for Naturalism and hence severely lowers its prior probability. Second, adding Evolution to our shared background knowledge won’t work because then every hypothesis, including Theism, equally explains the data. And third, if nothing else, the Theist could just add Evolution to Theism and the problem of evil vanishes.
Not every atheological argument from evil falls prey to these considerations. However, those that do have some explaining to do.