The Modal Ontological Argument is as follows:

(1) If God exists then he has necessary existence.
(2) Either God has necessary existence, or he doesn‘t.
(3) If God doesn‘t have necessary existence, then he necessarily doesn’t.
Therefore:
(4) Either God has necessary existence, or he necessarily doesn’t.
(5) If God necessarily doesn’t have necessary existence, then God necessarily doesn’t exist.
Therefore:
(6) Either God has necessary existence, or he necessarily doesn’t exist.
(7) It is not the case that God necessarily doesn’t exist.
Therefore:
(8) God has necessary existence.
(9) If God has necessary existence, then God exists.
Therefore:
(10) God exists.

The first bad assumption is found in premise one.  Before I demonstrate why, it is useful to define necessary existence.  Necessary existence implies an entity that exists in all possible worlds.  Leibniz coined the term when he put forth the idea that god created “the best of all possible worlds,” which is one of the earliest attempts to address theodicy or what is better known as The Problem of Evil.  Philosophers conclude that it is probable that god is a necessary being; however, that conclusion isn’t indicative of truth.  Therefore, it is a bad assumption to begin an argument with such an obscure probability.  Philosophers do not state how probable the necessary existence of god is.  It is probable that god does not have necessary existence.  That allusion can be found in premise two.  Also, one could just as easily argue “Either there are seven perfect beings which necessarily exist, or there are not” or any other random number of gods so long as we are able to begin with the unwarranted assumption that one can claim there are necessary beings.  Nothing but our intuition of simplicity is reason to choose one necessary being rather than seven or eight.  The possibility of god not having necessary existence is entirely ignored in premise seven — the second bad assumption and the worst of the two.  By what authority does one arrive at that premise?  Therefore, it follows that what comes after premise seven isn’t true.

God is believed to have necessary existence for a number of reasons; the greatest of these reasons is the assumption that he is eternal.  From there, believers posit that god’s existence doesn’t require an explanation.  Richard Dawkins and other atheists ignore this assumption when asking:  “where did god come from?”.  From a believer’s point of view, god isn’t a contingent being.  Therefore, that question is inapplicable.  However, there is a better option for us atheists and it’s the option we normally choose — perhaps without realizing:  god is an impossible being.  An impossible entity is an entity that doesn’t exist in any possible world (i.e. a seven sided octagon; a rectangular oval); it is the antithesis of a necessary entity.  With that said, I present the equally sound Modal Anti-Ontological Argument:

(1) If God doesn’t exist then he has impossible existence.
(2) Either God has impossible existence, or he doesn’t.
(3) If God doesn’t have impossible existence, then he necessarily doesn’t.
Therefore:
(4) Either God has impossible existence, or he necessarily doesn’t.
(5) If God necessarily doesn’t have impossible existence, then God necessarily exists.
Therefore:
(6) Either God has impossible existence, or he necessarily exists.
(7) It is not the case that God necessarily exists.
Therefore:
(8) God has impossible existence.
(9) If God has impossible existence, then God doesn’t exist.
Therefore:
(10) God doesn’t exist.

Of course, I’m making the same bad assumptions Theists make.  However, if they want to argue that their argument is sound, they must grant that ours is also.  Unlike the probability philosophers put forth, I can put forth a concrete probability:  it is highly probable that the Judeo-Christian god — the god that the Ontological Argument was designed to defend — does not exist.*  Thus, if this modal argument is sound, he has impossible existence.

I am aware that god is accepted as a necessary being.  However, that acceptance rests on three theological motivations:

1. God is a perfect being.
2. The Ontological Argument is sound.
3. Abstract objects depend on god in order to exist.

However, I don’t have these motivations.  The Judeo-Christian god is not a perfect being.  The Ontological Argument is unsound; keep in mind the definition of soundness:  an argument is sound if and only if it is both valid and all of its premises are actually true.  Finally, abstract objects (i.e. ideas, abstractions) do not depend on god in order to exist.  Therefore, I do not accept god as a necessary being, but rather, I consider god an impossible being.

Note:  My probability is based on numerous other factors that come from fields other than philosophy.  To be quite honest, I have concluded — without scintilla of doubt — that the Judeo-Christian god has impossible existence and thus, does not exist; that isn’t to say that it isn’t theoretically possible to have a change of mind given sufficient evidence.  I only drafted this argument because the Ontological Argument is still championed as a knock-down, irrefutable argument.  I beg to differ!

*For more info regarding my high probability, refer to the evidence tab.

Many thanks to doubtingmarcus for reviewing the argument and providing useful insight.