Where Theists Go Wrong in Their Thinking
Fine Tuning and Design:
They assume that the univerese is fine-tuned. Yet we can clearly see that 99.99% of it is very hostile to life. Life exists in the very few and very small places in which conditions allow. We exist in one such place. If you take a careful, objective look at life on this planet, you also clearly see flaws in design and many signs of an imperfect, blind process of selection. I often hear theists plead for us to look at the world around us and realize that it had to have been created by a conscious being. However they completely ignore perfectly adequate scientific explanations as well as being completely ignorant of the psychology which explains their reaction.
God of the Gaps:
Any gap in knowledge, whether it's a gap in science or just a gap in the theist's knowledge of science, is filled with something which is fabricated and has no real evidence. It is irrational to hold a belief without good reason. If something cannot be demonstrated to manifest in reality, it is indistinguishable from something which does not exist, and it therefore makes no sense to assert it as fact.
Evidence for God:
Many theists believe there is good evidence for god, and specifically the god of their particular religion. Aside from the design and fine tuning argument, the written stories are regarded as evidence (or outright proof). This presents a problem as this reasoning would necessitate belief in every mythology, every legend, every tale that has ever been written about. The only thing which can determine which one should be believed over all others is which culture, and what era one is born in. I could create a religion that was far more internally consistent, consistent with reality, and very morally sound and a couple thousand years later someone will find it and believe it to be true. And they will argue that the document I wrote (which had been copied many times) is evidence and they will argue that the consistencies with reality and real places and people I referred to prove that it is true. And they will reason that it contains superior morality which appeals to their sense of morality and it would be awful if it weren't true.
Personal revelation or religious experiences are also held up as evidence for god. However anecdotes do not a good evidence make, especially for something as far fetched as a god. We can easily find explanations for this: mental illness, sickness, drugs, brain damage, confirmation bias, suggestion, stress response by the brain, etc. Even if we had no other explanations, it wouldn't do anything to prove that the interpretation someone makes of such an experience is accurate. Miracles can be looked at the same way but with the added element of fraud, which is quite common with all religions (think: Ganesh statues oozing milk).