"In a world without God...why does evil exist?"

Christian professor Dr. Dan Lambert is using my book for a class introducing the students to atheism at John Brown University, which is an evangelical college. I've mentioned this before. His students wanted to know my answer to the above question.

Dan's full question is this:
Many of them want to know how you answer the problem from an atheist perspective. So, in a world without God, created and sustained by purely natural laws and evolving as scientists explain it, why does evil exist?
The short answer is that objective or ultimate evil does not exist. Everything that happens is natural. Nature destroys people on whom the existence of millions of lives depend as well as it destroys people who want relief from their painful existence. Nature is indiscriminate in its dealings with us without any meaning or purpose. This best fits what we experience, I think.

However, just because there isn't any ultimate evil doesn't mean there isn't suffering for which we think is unnecessary. On this view evil is suffering, intense suffering, suffering that turns our stomachs. If your students have a hard time contemplating this then don't use the word "evil" at all. Just use the word "suffering." I don't like to suffer. I don't want my loved ones to suffer, nor do I want their friends to suffer. As a human being who is part of the natural world who can reflect on this world I can have a say about the sufferings of myself and others. Since I don't like suffering I want to help alleviate the sufferings of others. I think that by doing so it increases the amount of pleasure for me in this world, since a world that doesn't have as much suffering is a world where I and the ones I love can have more pleasure. And pleasure, holistic Aristotelian pleasure, is it's own reward needing no additional justification.