In what he terms the "Freewill Argument for the Nonexistence of God" (FANG), atheist Dan Barker contends that the very definition of the Christian God is logically incoherent, and therefore the Christian God is nonexistent. Like many unsound arguments atheistic and otherwise, Barker's appears fairly convincing at a glance. In this case Plato's dictum bears repeating: "Arguments, like men, are often pretenders." The following is the main body of Barker's argument:
The Christian God is defined as a personal being who knows everything. According to Christians, personal beings have free will.
In order to have free will, you must have more than one option, each of which is avoidable. This means that before you make a choice, there must be a period of potential: you cannot know the future. Even if you think you can predict your decision, if you claim to have free will, you must admit the potential (if not the desire) to change your mind before the decision is final.
A being who knows everything can have no state of "uncertainty." It knows its choices in advance. This means that it has no potential to avoid its choices, and therefore lacks free will. Since a being that lacks free will is not a personal being, a personal being that knows everything cannot exist.
Therefore, the Christian God cannot exist. 
If we break down Barker's formulation further it goes something like this:
(P1) The Christian God is defined as omniscient and autonomous (having free will).
(P2) Autonomy and omniscience are contradictory.
(P3) Contradictions do not exist.
(C) The Christian God does not exist.
Premise P2 appears to be an intermediate conclusion reached on the basis of two additional supporting premises:
(i) Autonomy means the ability to make decisions, leaving future possibilities open.
(ii) Omniscience means knowing the future beforehand, precluding ability to make decisions.
(c) Autonomy and omniscience are contradictory.
The argument is admittedly valid. That is, the overall conclusion does appear to follow logically from the premises and sub-premises. But is it sound, or necessarily true? To answer that question, we must examine the premises individually. P1 turns out to be basically what I would term a "zero-sum" definition of God, in which his "omni" characteristics (in this case omniscience) are held to be self-contradictory because they are all-consuming. "God is defined as a personal being who knows everything." Barker's "definition" sounds reasonable enough, but his particularistic interpretation is not supported by Christian theology, by biblical hermeneutics or even by most standard English dictionaries. Thus Barker's definitions of God and omniscience appear arbitrary, perhaps chosen in order to support a presupposed conclusion. Theologically, the concept of God is a transcendent personal being (an eternal personality, for lack of a better word) who possesses or exhibits attributes such as omniscience. Personalities cannot be ontologically reduced to definitions of their descriptive attributes.
This appears to be one reason atheists often clamor for a "definition" of God – in order to play verbal games with the particular words chosen to define him. Concepts do not perfectly convey definitions; to the contrary, definitions imperfectly convey concepts. To misunderstand this is to reduce substantive reasoning to quibbling, and lend credence to logical fallacies such as equivocation. For example, a debater on alt.atheism (many years ago now) argued along these lines: "Omnipotence means all power; but if God has all power, then humanity has none, and therefore God is directly responsible for all the evil and suffering in the world." Here "omnipotence" does mean "all power," but not in a zero-sum sense. "All power," at least in theological terms, means unlimited capacity on the part of God to do whatever he chooses. The former definition precludes free will. The latter does not. God is described by theologians as "omniscient" because he is said to have knowledge of what is ordinarily quite beyond the reach of human understanding – things like the motives of his followers and the respective geopolitical futures of the nations. Terms like "omniscience" thus serve the purpose of theology by contributing to our understanding of God as revealed in Scripture, but implicit in the understanding is that God is not shackled by definitions of words coined in order to describe him in the first place.
Consider a counterexample: Dan Barker refers to himself as an "atheist." My old desk dictionary, Merriam-Webster's Tenth Collegiate, defines an "atheist" as "one who denies the existence of God." That same dictionary then offers this definition of "deny": "5: to refuse to accept the existence, truth, or validity of." So it could be argued that according to a dictionary definition, an atheist is one who simply refuses to accept the existence of God or the truth of his existence. It gets worse. My dictionary also defines "denial" in these terms: "6: a psychological defense mechanism in which confrontation with a personal problem or with reality is avoided by denying the existence of the problem or reality." By carefully selecting the definitions of the words used to define an "atheist," I can prove that Dan Barker's "atheism" is really a psychological defense mechanism by which he avoids confrontation with the reality of God's existence.
Barker argues in premise (ii): "A being who knows everything... knows its choices in advance." I would answer that Barker's premise is both irrelevant and invalid: First, if free will is really the ability to make decisions, then it cannot rightly be debunked on the grounds that decisions themselves delimit free will. As a bachelor, for instance, I considered myself "free" to choose a bride, but now that I have made my choice I have freely renounced all other choices. My decision here is no violation of free will, but is rather the very consequence of it that gives it meaning according to Barker's own definition. God likewise makes meaningful choices precisely because He is free to do so. Second, the assertion that an omniscient being "knows its choices in advance" is a straw man, because God is said in Scripture to inhabit eternity, not time. An omniscient being (particularly the God of Scripture) would not subsist in the space-time continuum of the physical universe, subject to the constraints of time and entropy, but rather outside it as its creator. Christian theism involves belief in a transcendent God, the very sort of entity physicists such as Stephen Hawking must at least consider when they speculate what could possibly cause, or at least explain, the birth of space and time at the point of the big bang singularity. God does not know His own future because He has no future. Because Barker's theological construction is itself incoherent, his argument collapses.
On the other hand, if verbal constructs can be said to have legitimate existential import then there are some powerful arguments available for the existence of God. Most famous of these is Anselm's ontological proof, more coherent than Barker's FANG and in more sophisticated forms enjoying the endorsement of noted logicians such as Alvin Plantinga, Kurt Godel and Charles Hartshorne. Anselm's original version from the Proslogion goes as follows:
[I]t is quite conceivable that there is something whose non-existence is inconceivable, and this must be greater than that whose non-existence is conceivable. Wherefore, if that thing than which no greater thing is conceivable can be conceived as non-existent; then, that very thing than which a greater is inconceivable is not that than which a greater is inconceivable; which is a contradiction.
So true it is that there exists something than which a greater is inconceivable, that its non-existence is inconceivable; this thing art Thou, O Lord our God! 
That is, to properly conceive of God (as the greatest conceivable being or necessarily existent being) is to logically ascertain that His non-existence is inconceivable. If valid ontological proofs (or disproofs) are conclusive, as Barker seems to believe, then God is not incoherent but necessarily existent. If such proofs are not conclusive, then Barker's FANG argument proves nothing anyway.
 Dan Barker, "The Freewill Argument for the Nonexistence of God," Freedom from Religion Foundation, https://ffrf.org/legacy/about/bybarker/fang.php.
 Anselm, "Proslogion III," cited in Henry Bettenson and Chris Maunder, eds., Documents of the Christian Church, New York, Oxford: 2011, p. 145.