There's nothing contradictory about it. But I am saying it is an affirmative assertion despite involving a negative clause.
And yet there is no negative clause implied in the assertion God exists! Its a claim to the truth. And despite the grammatical form of God does not exist it is only a conclusion that can never be fully justified, since it is logically impossible to demonstrate the actual non-existence of that object (although propositions can be demonstrated as false), whereas if God does exist then logically it must be possible to demonstrate his existence. That is the crucial distinction. Therefore God exists bears the burden of proof.
In other words, the idea that God exists must itself exist in order for the reverse claim to be possible? And?
If you were to present to me a wordview that you'd like me to adopt, and an essential aspect of that wordview is strong atheism; I'd certainly be justified in asking you to demonstrate that atheism.
Let me rephrase. If you are going to claim that strong atheism should be the rational default, why should you be except from the same demand as if I were to insist that theism be the default?
Thats not my argument. Atheism is founded on facts, in other words inferences from the experiential world that can be true or false, thus every experiential statement is therefore contingent, and it follows then that God does not exist is a contingent statement. The theist makes no such concessions to the experiential world but proposes that God transcends the world of experience, and therefore God exists is given supposedly as a truth statement.
But what makes you so sure that no one has not has had direct experience of the 'supernatural'. There is no evidence for the supernatural that will play into a modern, replicable framework of scientific reductionism, but tell that to the priest that cures blindness, exorcists who have encountered the demonic, visionaries who have had direct converse with religious figures.
I can't prove any of the above (that's not my point) but when you really start looking into these things more and more the idea that it's all fraud and fantasy is just not convincing. (even though there is much of that involved)
All you are referring to is subjective experience and a will to believe-as-faith. Im talking about objective evidence, evidence upon which we can all agree, such as that that the sun rises in the morning and wanes in the evening, that water is composed of two molecules of hydrogen and one molecule of oxygen, that all living matter eventually degrades and dies; but even if we leave aside the properly scientific aspect there is still no objective evidence of miracles or the supernatural, for there is neither a body of facts nor any information that conveys to us knowledge of the supernatural other than on anecdotal or reported terms. And many of the experiences, as you acknowledge, have been spurious or recognised as having a psychological explanation.