The Ontological Argument for the Non-Existence of God

In doing research for my upcoming book (The Authority of Faith), I've encountered innumerable lines of argumentation that attempt to rectify revelation with that of the world of reason.  These claims of revelation, at every point to which they can be tested are demonstrably false.  Some are so blatantly contradictory that they implode in their own incongruities.
One such argument, which I always have found to be particularly dubious was the line of argumentation used by St. Anselm in defending claims of god's existence.  The Ontological Argument for the Existence of God, as it is known is a response to Anslem's inability to grasp with the incomprehensibility of how the wrold came to be.  Through his astonishment of the spectacle of the natural world Anselm posits his claim about the nature of god.

1. If I am thinking of the Greatest Being Thinkable, then I can think of no being greater

1a. If it is false that I can think of no being greater, it is false I am thinking of the Greatest Being Thinkable

2. Being is greater than not being

3. If the being I am thinking of does not exist, then it is false that I can think of no being greater.

4. If the being I am thinking of does not exist, then it is false that I am thinking of the Greatest Being Thinkable

Conclusion: If I am thinking of the Greatest Being Thinkable, then I am thinking of a being that exists

Wikipedia

This line of reasoning is flawed for a number of reasons, although I think that his line of argumentation we can find a necessary conclusion which is contrary to the claimed intent of the argument.
#2   Existence is greater than non-existence.
This premise will be worth our focus. I would contend that this greatest being, with the powers, of omnipotence, universe creation, omniscience and omni-benevolence  I think it would be an even greater miracle, an even more amazing force which is omnipotent, and can be the cause of the existence of the universe, and has the quality of non-existence.  A god who possesses the quality of non-existence, yet had the power to create this universe, would be a more powerful god
A god who could create our universe, but didn't event require the quality of existence for this task is an even more marvelous, even more astounding feat to accomplish. 
Regardless of the numerous ways in which the ontological argument fails, we can see the absurdity in every aspect of examination we choose to employ.
Edit:  There is a reference to this line of reasoning made by Douglas Gasking in the Stanford Encyclopedia of Philosophy.  I'm not the first to come up with this...