Without God, morality is just feeling. The speaker argues that objective moral truths can only exist if God exists. Claiming an action is intrinsically evil, not merely distasteful, assumes God is real.
Chapters
So the title of the book is If There Is No God... The Battle Over Who Defines Good and Evil. What we have today is feelings versus moral truths. We don't have it in math. If you feel that 2 and 2 is 5, it's irrelevant. But if you feel in the moral realm, that's perfectly legitimate. In other words, we acknowledge scientific and mathematical truths, but we don't acknowledge moral truths. And there are only moral truths if there is a God. Otherwise, all morality is feeling, and people have to recognize that. So here is the way it works. If there is a God, there is good and evil. They really exist. There are moral truths. And if there are moral truths, then there is a God. If you claim that certain things are good, certain things are evil, independent of how you feel about it, you are in effect affirming God.