"What do you think is the error of thinking in atheism? Where do you think we all go wrong? I am curious about this."
The answer is below the line. It is a much more elaborate answer than I anticipated, which raises many points. I withhold my opinions here, and his name, so that everyone can peer into the opinion of the opposite side of the god debate, as I did when I first read this response.
It seems to me that most atheists do not to think the implications of their worldview through. They do not follow the logical consequences of it. Few great atheist philosophers did, but somehow the street-atheist seem not to be interested in their conclusions. I'm referring to matters like values, meanings, purpose, rationality, epistemology, free-will, the existence of the self, etc.
Many atheists think that it's either atheism or Christianity. They seldom contemplate the idea that God, even a loving one, might exist even if many, if not most, of the things found in the Bible were false. Many things which atheists, and me, hate about the Bible could be false, and God still exist (examples: hell, homophobia, killing of innocent people, slavery, outrageous punishments, etc.).
Many atheist demand physical evidence of God, which for the theist is contradictory. The theist regards God to be a spiritual being. No physical evidence could be ever provided. God, being non-material, could not ever be analyzed by science or physical methods.
Many atheists think that science found all the answers or will do so eventually. Especially to fundamental, transcendental questions. They don't entertain the idea that many questions are not of scientific nature at all.
Many atheists think that because most believers believe in things which can not be proven or make no sense, therefore God does not exist. The mistake here is to dismiss something which could very well be real is a “spiritual” sense, but wrong “intellectually”. For example, if you said “I love my partner” and I asked you for reasons, you could give me some but they might all be “wrong” (not subjectively wrong, really wrong). It would not invalidate your experience.
Many atheists insist that on one hand we are machines/automata without free-will, and on the other hand we have values, ideals, morality and responsibility. It seems contradictory to me.
Many atheists simply don't like the idea of there being a God, but are not honest enough to admit it.
Many atheists are more concentrated in dismissing, rather than evaluating and considering, evidence for the existence of God.
Many atheists will try to find another explanation, no matter how speculative, to systematically eliminate the possibility for there to be a God. Even where God, as a possible explanation, would have been a simpler explanation than the alternative. A good example of this would be the Multiverse theory.
Many atheists have too much confidence in science, and tend to ignore areas where science has failed and another explanation might be more plausible. But any explanation involving a personal agent as a cause is systematically rejected a-priori, maybe just because it would be no longer explainable by science only. They insist, no matter the evidence, that the explanation must be naturalistic.
Many, if not most atheists, are very less inclined at looking at the cumulative case, the “big picture”, offered by theism. They rather prefer to attack theism in isolated chunks, believing that addressing all the points separately, then theism has been shown false. The thing is, that theism as a whole presents a rather good cumulative case. This is seldom addressed.
Many atheists think that theists presume to have all answers. Even in theological questions. This is not the case. We are very ignorant about religious matters and don’t claim certainty in many areas.
Many atheists think that only bad things can result from religion, and fail to recognize that many good deeds were also motivated by religious beliefs. True, many things were committed in the name of religion. It does not prove, however, that theism is false. Just that people are capable of being evil and/or stupid.
Most if not all atheists dismiss the personal religious experiences told by theists on the basis of being false, delusional, or something like that. They are more keen at dismissing away these experiences than to consider the possibility that some of them might be true.
Many atheists think that it's about an intellectual discussion. Theists are not there only to discuss and prove somebody wrong. Theists don’t derive their sense of self-worth from winning arguments, or at least they should not.
Many atheists believe there is a (false) dichotomy between science and religion. That for one to be "true" the other has to be "false". Less drastic than this, is the view that science and religion conflict with each other. True religion should be sympathizing with science, but indifferent to it. True religion, on the other hand, should be very concerned about the scientist. True religion is about the personal relation of the individual with God and one another, about spiritual values and growth. Unfortunately many religions are "corrupted" and do make claims about scientific reality. That should be left to science. Consider: if God is true, did he not have created the physical world as well? He would be the ultimate scientist/engineer and hold these activities in high regard.
Many atheists believe that science proves that religion is false. Science might have proven that certain ideas (superstitions) associated with religions were false, but the inference can not be done that science proves that there is no God and can not be. It will even remain a philosophical / metaphysical question.
Many atheists believe that faith means believing in something in spite of evidence to the contrary. But if you ask a theist they will give you another definition completely. Regardless of whether the theist is justified in their beliefs, this difference in definition / interpretation of the word "faith" leads to a lot of misunderstanding and false accusations on part of the atheist. Usually no effort is done to see what the theist means.