In Part 1, I discussed why evangelizing the atheistic worldview is actually inconsistent with the very worldview it is promoting. I concluded it with mentioning that the challenge could be flipped back on the Christian in a heartbeat. In Part 2, I will show you how to answer that challenge and place the ball back in their court.
Let me start by reiterating the challenge by the atheist: "You claim your God is omnipresent (everywhere); He sees everything that you do; yet you sin. That must mean that you don't believe your worldview at its core either. If you don't ultimately believe your worldview, why do you expect me to?"
There are a couple ways this could be addressed. The more logical would be to make them aware that their challenge is not the subject of the conversation and they are just avoiding the real point by trying to focus on the Christian worldview.
But, most of the time, that won't work. This challenge is not a logical challenge. It is more of an emotional challenge. There is more underneath that challenge than meets the ear. Their concern is that so many Christians teach one thing, but act another. They will typically use the word "hypocrite". They believe that this is a good challenge and they believe that they have you nailed down because you pointed out an inconsistency in their worldview, and they believe they are justified in pointing out the same in your's.
Here is where they are mistaken, though. The Christian worldview does not teach that once someone accepts Jesus Christ as Lord and Savior that they become perfect and unable to sin or make mistakes. The apostle Paul said that there were many times he would be frustrated with himself because he does things that he knows he shouldn't and doesn't do things he knows that he should as a follower of Jesus Christ (Romans 7).
When you are discussing this with the atheist, make sure that you clear up that misunderstanding about the Christian faith. When the expectation of perfection is removed, then he essentially has no argument. You will need to reassure him (her) that this is not a "cop out" or "excuse" to do bad things, but that it is an assurance that we will not be condemned to damnation by Christ because we do bad things. Also reinforce that the Bible teaches that followers of Christ to strive to follow His teachings as best as they can- but it is understood that this is impossible, and that is why we needed Christ to take the punishment for us. I would also include something along the lines that anyone who teaches that, "Because of the assurances of heaven through belief in Jesus Christ I am allowed to do whatever I want and still know that I am forgiven and will go to heaven," are in direct conflict with the teachings of Christ and the apostles.
At this time, you should ask if there are any questions that you need to answer or clarify. Once you have established that there actually is no inconsistency in the Christian worldview, you are free to challenge him to clear the inconsistency in his own worldview.