The key to understanding this is that they think there is evidence for a god. They'll often say that we are "surrounded" by evidence. They solidly believe we are in denial because the evidence is so overwhelmingly obvious that a god exists.

We're all subject to our world views, even atheists. The human tendency is to reinforce that world view, and to select evidence that confirms what we already believe.

If you've encountered such a person, the problem lies deeper than simply spouting "facts" at one another. You need to dig deeper, because the person may be confused on an epistemological level - the philosophical basis of how we go about knowing things.

For example, what is evidence? Could you explain it? Do you know what the Standards of Evidence are? Or that different studies/fields have different studies? Can you explain why the standards are the way they are? Do you know how a scientific case is made?

These are difficult, complex questions, and not everyone has bothered to consider them.

For many theists (and atheists - we have plenty of ignorant people ourselves), their understanding of "evidence" seems to be "anything that is consistent with my claim".

The scientific-minded person would then ask whether that evidence uniquely supports one possibility over another, or whether the connection between the evidence and the claim contains logical fallacies, etc. For many, they simply stop at the point where their proposition seems supported, without any further examination. If one's epistemic background too dysfunctional, one can go through life falsely believing there's sufficient evidence for a claim, where none actually exists. From their perspective, you're the one who's irrational.

Combine the above with rationalizing away inconsistencies in that world view, and you've got a ripe case of Confirmation Bias[1]. We're all prone to this. The question is whether one is in the habit of ensuring our "facts" and approach are accurate.

America is not known for widespread rudimentary education on skepticism, critical thinking or epistemology, for example. If you're arguing with such a person, you may need to provide that basic education.

But be careful not to trivialize their position. They aren't dumb - they are complex individuals with varied backgrounds and experiences. They are mistaken about having any "good evidence" supporting their notions about a god. The next question is "why"?