According to the Watchtower publication Insight,
This Word, or Lo′gos, was God’s only direct creation, the only-begotten son of God, and evidently the close associate of God to whom God was speaking when he said: “Let us make man in our image, according to our likeness.” (Ge 1:26) Hence John continued, saying: “This one was in the beginning with God. All things came into existence through him, and apart from him not even one thing came into existence.”—Joh 1:2, 3.
Source: http://wol.jw.org/en/wol/d/r1/lp-e/1200004625
The publication states that the λόγος was God's only direct creation, the only-begotten son of God." Furthermore, it also identifies the λόγος as Jesus Christ.
This Word, or Lo′gos, was God’s only direct creation, the only-begotten son of God, and evidently the close associate of God to whom God was speaking when he said: “Let us make man in our image, according to our likeness.” (Ge 1:26) Hence John continued, saying: “This one was in the beginning with God. All things came into existence through him, and apart from him not even one thing came into existence.”—Joh 1:2, 3.
Source: http://wol.jw.org/en/wol/d/r1/lp-e/1200004625
The claim is that God's λόγος, the Word of God (ὁ λόγος τοῦ θεοῦ), is a creation (and thus, a creature). If God's λόγος was created, then it did not exist before it was created. The corollary is that God at one point lacked λόγος, or was ἄλογος. The Greek word ἄλογος means "without reason, logic; irrational; illogical."
Source: http://www.blueletterbible.org/lang/lexicon/lexicon.cfm?strongs=G249; http://www.perseus.tufts.edu/hopper/morph?l=a%29%2Flogos&la=greek#lexicon
The Greek letter α (alpha) prefixed to a word signifies absence, opposition, or negation.
Source: http://www.blueletterbible.org/lang/lexicon/Lexicon.cfm?Strongs=G1&t=KJV
For example, the Greek word νόμος (nomos) means "Law." When prefixed with the Greek letter α, it means "without law; lawless."
Source: http://www.blueletterbible.org/lang/lexicon/Lexicon.cfm?strongs=G459
While the Greek word λόγος is most often translated simply as "word," it also possesses the meaning of "reason" and "logic."
Source: http://www.blueletterbible.org/lang/lexicon/Lexicon.cfm?strongs=G3056
Something which possesses reason, or the ability to reason, is said to be "rational."
Source: http://dictionary.reference.com/browse/rational?s=t
Something that lacks reason is said to be "irrational."
Source: http://dictionary.reference.com/browse/irrational?s=t
The consequence of the argument that God created the λόγος was that God was at one point ἄλογος, or without reason, illogical, or irrational.
How do Arians and/or Jehovah's Witnesses respond when it is said that their God was without reason, irrational, and illogical?
What does this say about God's supposed immutability?