Warning- I have never formally studied theology or ethics, the following are purely the thoughts and speculations of an amateur, an 'armchair theologian' if you will.
Part 1. The existence of evil from an atheistic perspective
To start off, we need to figure out what atheists mean by 'evil'. A common theist argument is the existence of certain core universal moral values, implying an objective morality, and therefore a source for that morality. The reply is that these are merely the natural result of budding, burgeoning societies, and that these ‘universal morals’ are actually just behavioural adaptations to living in increasingly large and complex social groups, and which aid cooperation between individuals and groups of individuals, helping ensure the survival of these groups and individuals in the best Darwinian traditions.
Well okay, but in that case what the atheists are telling us is that those things which we label as ‘evil’ aren’t really. They are merely things that impede social cohesion and cooperation. We call murder ‘evil’ because if everyone went around killing people when they felt like it, your society would swiftly collapse. Likewise stealing, or lying, or random destruction of property. However, these things are not in reality ‘evil’. There are no evil things; there are no good things. There are just things, which are either beneficial or harmful for one group or individual than other things, and what is beneficial for one individual or group may be harmful to another. After all, the tribe in the next valley may not be so keen on your social cohesion and cooperation when your well-organised army invades their village!
By appealing to evolutionary science, atheists have intentionally removed the concept of objective morality from the equation. They say that if God is good, He wouldn’t allow evil, while at the same time claiming that there’s no such thing.
A possible answer to this may be that although the atheist does not believe in evil, as a believer in objective morality themselves, the theist does, and so needs to explain it. Fair enough. That's what I'll be trying to deal with next.