When you say Pitre “argues quite persuasively for the traditional authorship,” do you mean he succeeds in establishing that authorship beyond all reasonable doubt, or is he making the more modest assertion that Matthew, Mark, Luke, and John are, in fact, quite likely to have been the true authors, despite all the arguments that have been put forward over the years contesting that claim?
Pitre argues the point from number of angles, but here is just a sample from the early Church Fathers:
Early Fathers on the Origin of Matthew
Papias of Hierapolis:
Matthew composed the sayings in the Hebrew dialect and each person interpreted them as best he could.
Justin Martyr:
For in the Memoirs of the apostles and their successors it is written…
Irenaeus of Lyons:
Now Matthew published among the Hebrews a written gospel also in their own tongue while Peter and Paul were preaching in Rome and founding the church.
Clement of Alexandria:
Of all those who had been with the Lord only Matthew and John left us their recollections, and tradition says they took to writing perforce. Matthew had first preached to the Hebrews, and when he was on the point of going to others he transmitted in writing in his native language the Gospel according to himself, and thus supplied by writing the lack of his own presence to those from whom he was sent…”
Early Fathers on the Origin of Mark
Papias of Hierapolis:
And the elder [John] used to say this: “Mark, having become Peter’s interpreter, wrote down accurately everything he remembered, though not in order, of the things either said or done by Christ. For he neither heard the Lord nor followed him, but afterward, as I said, followed Peter, who adapted his teachings as needed but had not intention of giving an ordered account of the Lord’s sayings. Consequently Mark did nothing wrong in writing down some things as he remembered them, for he made it his one concern not to omit anything that he heard or make any false statement in them.”
Justin Martyr:
We are told that he [Christ] changed the name of one of the apostles to Peter, and it is written in his memoirs that this took place…”
Irenaeus of Lyons:
After their [Peter and Paul’s] departure, Mark also, the disciple and interpreter of Peter, himself handed down to us in writing the things which were preached by Peter…
Clement of Alexandria:
But a great light of godliness shone upon the minds of Peter’s listeners that they were not satisfied with a single hearing or with the oral teaching of the divine proclamation. So, with all kinds of exhortations, they begged Mark (whose gospel is extant), since he was Peter’s follower, to leave behind a written record of the teaching given to them verbally, and did not quit until they had persuaded the man, and thus they became the immediate cause of the scripture called “The Gospel according to Mark.” And they say that the apostle, aware of what had occurred because the Spirit had revealed it to him, was pleased with their zeal and sanctioned the writing for study in the churches.