The reason for arguing that modern western atheism is incoherent is not that it is irrational to disbelieve in God; I think that one can be entirely sane and rational and disbelieve in God (although I actually think that agnostics have beliefs that are much more consistent with pure rationality than either theists or atheists, but that's a side note).This is not dissimilar from the evolutionist who firmly believes in human equality and asserts race is a myth, failing to grasp that he simply cannot rationally subscribe to both articles of faith.
No, the reason that modern atheists have incoherent views is that they simultaneously
- assert that there is nothing beyond that which is visible (i.e. they are materialists)
- they believe in rights, and not merely in a legal or social descriptive way, but in an absolute and prescriptive way.