Back at square one, what do atheists claim? The third kind of atheistic claim is: “I do not believe in GOD.”
This claim recognizes that it is theoretically possible that GOD exists, and also acknowledges that there is evidence for GOD’s existence.
But whoever makes this claim is not convinced by the same evidence. Such atheists may have examined the claims thoroughly, reviewed the pros and cons, and concluded that they are not inclined to believe them even though they could not completely disprove them because, if such a refutation existed, the theistic philosophers would probably have acknowledged it and withdrawn from their support of this evidence.
But since they were also not completely convinced of them (perhaps because they hold other assumptions), they finally chose not to believe in GOD.
On the face of it, this is a perfectly legitimate position. Life often requires making a decision, even though the conclusive proof is lacking. As viable possibilities are identified for making a choice, the various options are evaluated and the one that seems the most compelling is chosen. Just as people can be persuaded to believe in GOD, even though they know that the claim is against theism, so they can be persuaded not to believe in GOD, even though they know that there is evidence for GOD’s existence.