There is literally no way anyone is going to be able to do this in the limitations of a blog - if you can get through Michael Martin's "Atheism: A Philosophical Justification" you'll know the answer. Dawkin's "The God Belief" is shorter and easier because he uses evidence to shorten the strictly logical disproofs philosophers use. An older and less complete, but more readable, philosophical disproof is George H Smith's "Atheism: The Case Against God". There are others, but of the ones I've read these two are the best and the most accessible, respectively.