1. It lies about the nature of the books we have – reports and narratives by witnesses of words (most of them anyway) spoken in another language, and already someone else’s words by the time they reach us.
2. It overthrows the nature of scripture. The whole canon is the locus of inspiration and witness to revelation.
3. It denies the incarnation. The whole point about the nature of gospel as witness to the Word made flesh is that Jesus’ deeds do God’s work, and his words are one part only of the story. Story is the category through which we know Jesus, not dictation, because we need to see and know God’s life lived out in human flesh and not simply instructions dictated in a vacuum. The stories are not just a rather unimportant framework for the words; the stories are the essence of the god news of the incarnate Word.
Also read Peter Head's defence of the red letter bibles and a subsequent discussion here.
In the comments to this post, Stephen Carlson pointed out that Chaplin's arguments against red letters "also argue against the modern practice of using quotation marks in the narrative" for the following reasons:
(1) Just as the red lettering mark words Jesus didn't actually say (because he spoke in Aramaic), so too are the words in quotation marks not really the exact words of the speakers especially in the gospels.
(2) Just as red lettering give focus to Jesus' words over others, so too do quotation marks give focus to some words of the biblical text but not to others.
(3) Just as red lettering distinguish Jesus' words (in red) from his actions, so too do quotation marks.
Peter Williams points out that many languages manage without speech marks and before the twentieth century English Bibles managed well without them.
Chaplin has responded to Carlson on his blog Red Letter Bibles strike back arguing that quotation marks are not to same. However, he concludes that "it might be possible to construct a purist argument that all our texts should be written in a largely unpunctuated stream of uncials … BUTIDONTTHINKTHATWILLCATCHON."