Unfortunately, I could not read the entire thread before posting. Too long. Basically, you are asking for positive evidence that atheism is a more reasonable position to take than theism. It is reasonable to point out that theism bears the burden of proof, but the OP is really asking to go beyond that. After all, many believers honestly think that there is reasonable evidence to prove the existence of their particular god or gods, so burden-of-proof claims seem unconvincing to them.
There is no single best reason for rejecting belief in gods (other than the generic "lack of evidence"), but I can list some here. I take gods to be undetectable, immaterial, intelligent agencies that have absolute control over some aspect of reality. Note that the following points are reasons to reject belief in gods, not absolute proof that no gods exist.
- Human souls (i.e. minds) cannot exist independently of physical brains according to the preponderance of evidence about mind/brain interactions. That is, brainless minds likely do not exist.
- Too many gods. Too many mythical beings. Humans have a long record of making up the existence of false gods. They are notoriously bad god-detectors. Hence, any particular god is likely to be a false god.
- No evident interaction between gods and physical reality. Reported miracles invariably turn out to be false or completely uncorroborated by empirical investigation. If gods were real, one would expect to be able to detect their interactions with reality.
- Gods are unnecessary explanations for natural phenomena. There are no natural phenomena that seem to require belief in a god to explain (although there seem to be many such phenomena to less scientific cultures).
- Prayer does not work. People who pray do not seem to be luckier than those who do not, although one would expect their prayers to have some beneficial effect if there were a god to grant the wishes.
- The argument from design--a very powerful argument for a creator god--fails in the face of evolution theory. That is, natural selection provides a more satisfying explanation of the origin of biological diversity.
- Failure of revelation. Religion invariably spreads from a single geographical point outwards, which is the pattern we would expect if the origin of religious belief were invented by individuals. If there really were gods, then we could reasonably expect the same gods to be discovered simultaneously in different locations. (That is, it is unlikely that a god wishing to make itself known to humans would rely just on one person or group to spread the news.)
- God of gaps phenomenon. Historically, scientific arguments have always trumped religious and superstitious claims, because people have discovered that belief in natural explanations gives better results. The trend to give up supernatural explanations in favor of natural ones suggests that supernatural explanations are just plain wrong.
These points tend to overlap somewhat, and they are not exhaustive. They are indicative of the type of argument that I, as an atheist, would bring to bear against belief in gods. It is not that I can disprove the existence of gods in a mathematical or logical sense, but I do believe I can show them to be as unlikely to exist as other mythical beings that people have come up with.