The worst argument that‘a believer in god can use is the negative proof i.e. when she says “can you prove god doesn’t exist?”- the answer to this is that the onus is on the one asserting a belief to positively prove that to which they assert. We are familiar with this concept in other areas of our society. If we are unfortunate enough to be charged with a crime how unjust would it be if you were told that the prosecutor was not going to adduce any evidence that you committed the crime but you have to prove that you did not break the law?
If this argument is brought to its natural conclusion it can enter into the realm of absolute absurdity. The mere fact that a proposition cannot be disproved does not render it true. This is known as an argument form ignorance which is a logical fallacy- X cannot be proved false therefore it is true. There are innumerable things that you do not believe in that cannot be shown do not exist. Bertrand Russell deals with this question delightfully in his essay “Is There a God?”
If I were to suggest that between the Earth and Mars there is a china teapot revolving about the sun in an elliptical orbit, nobody would be able to disprove my assertion provided I were careful to add that the teapot is too small to be revealed even by our most powerful telescopes. But if I were to go on to say that, since my assertion cannot be disproved, it is an intolerable presumption on the part of human reason to doubt it, I should rightly be thought to be talking. If, however, the existence of such a teapot were affirmed in ancient books, taught as the sacred truth every Sunday, and instilled into the minds of children at school, hesitation to believe in its existence would become a mark of eccentricity and entitle the doubter to the attentions of the psychiatrist in an enlightened age or of the Inquisitor in an earlier time.
There are infinite things that are things that cannot be disproved but we do not therefore accept that they are true. In fact taking this position belies all methodology that has advanced our understanding of our Universe. Russell’s teapot is the foundation for numerous incarnations of gods which have arisen to highlight the lunacy of this logic: Invisible Pink Unicorn, flying spaghetti monster. Religious people also try to use this logical fallacy when they say that “You are assuming god is false because we cannot prove he exists” I am not 100% sure that god doesn’t exist–no one is this is an epistemological problem; can we ever be 100% sure about anything?
By using evidence I can explain with greater quality the nature of our universe. The 14th centaury logician William Ockham provides a method of logical reasoning known as ‘Ockham’s Razor’ in which he states that the explanation of any phenomenon should make as few assumptions as possible. Therefore where evidence explains our universe this implies that where there is no evidence to the contrary this solution is valid.
 Russell, B., “The Collected Papers of Bertrand Russell” Slater, J. G. and P. Köllner Eds. (McMaster University ed G. Allen & Unwin, 1983)