When it comes to debating with atheists, we must recognize that for atheists, their arguments against God are of the upmost of importance. Their entire lives and eternal future (or lack thereof) depend upon them being right. It is vital for mankind to be nothing more than a globule of chemical reactions. It is absolutely essential that Christians are wrong in their worldview and declaration of a holy God.
In the process of their declarations of being right, they do contradict themselves and prove the Christian’s point: moral positions never evolve from chemicals, but come to us from a God who has declared to us what is right and wrong, good and evil. Yet, we must recognize that all the logic in the world will never convince them otherwise, they have far too much to lose. So when we point out their logical inconsistencies, we know that they will reject what we say. That is a given.
What it takes for the atheist to be saved from his spiritual foolishness is true conversion. They need a new heart, eyes to see, ears to hear, and new breath. That can only come from the Holy Spirit moving in them as the word of God is faithfully preached. The same was true for us back when we were agnostic or atheistic in our views. While we may improve on our understanding of logic, and our debating skills, the conversion of the atheist is completely outside our ability. They need a grace that only God can give them. As long as that grace is absent, the atheist will press on with a religious zeal in his false views of the world around us.