They claim the most common response they receive from Christians is, “If the story is false or embellished as you speculate, why would early Christians die for a story that was obviously untrue?”
I must admit that I agree with the author in that simply claiming that people becoming martyrs over the belief that something is true does not in and of it self make it true. In example they give the Muslims. Muslims indeed martyr themselves for a belief they hold, which any Christian must confess disagrees with the Word of the True God, I AM. Yet it could be noted that Christians usually become martyrs by the hands of others, whereas Muslims usually become martyrs by their own hands.
A quick source [Christistheway.com] followed by a more detailed source [bible.org] for each gospel:
Matthew, Matthew: Introduction, Argument, and Outline
Mark, Mark: Introduction, Argument, and Outline
Luke, Luke: Introduction, Outline, and Argument
John, John: Introduction, Argument, Outline
Above the actual author, date, and eyewitness account is the inspiration of God whereby the Holy Spirit moves elected persons of God to write that which are the Words of God.
2 Timothy 3:16 All scripture is given by inspiration of God, and is profitable for doctrine, for reproof, for correction, for instruction in righteousness: 17 That the man of God may be perfect, thoroughly furnished unto all good works.
Being inspired [God breathed]; this ensures that the author, though able to use their own style of writing and experiences are moved by the Holy Spirit without error to write the inerrant infallible things of God. They do not simply write all that they know or want to, but that which the Holy Spirit gives them utterance [2 Peter 1:20-21].
Secondly, time is not a factor, for the Holy Spirit (being of the Trinity) knows all, and is able to give man total recall of all that was, is, and will be, to the desire of God’s purpose. Christ gives this promise to His followers in John 14:25 These things have I spoken unto you, being yet present with you. 26 But the Comforter, which is the Holy Ghost, whom the Father will send in my name, he shall teach you all things, and bring all things to your remembrance, whatsoever I have said unto you.
Thirdly, for the sake of the authors, Matthew and John were for sure eyewitnesses to the ministry, death, burial, and resurrection of Jesus Christ [Matthew 10:2-4, 1 Corinthians 15:4-6]. As for Mark and Luke, the above links can be viewed for more information but their gospel accounts (though some may go to great links to show where they vary) leave no margin of variance that can be deemed as proof that they are uninspired or made up.
This is a good question, but does not prove their idea that the argument of circular reasoning must discount the inspiration of Scripture, for their argument also attacks the very ideas of science itself which they deem to think right.
"The rocks do date the fossils, but the fossils date the rocks more accurately. Stratigraphy cannot avoid this kind of reasoning . . because circularity is inherent in the derivation of time scales."—*J.E. O'Rourke, "Pragmatism vs. Materialism in Stratigraphy," American Journal of science, January 1976.
Agnostic asks whether biblical Christians commit circular reasoning.
Dating Rock Layers