Farrer Theory as a basis for increased skepticism toward Matthew:
The Farrer hypothesis (also known as the Farrer-Goulder-Goodacre hypothesis) is the theory that the Gospel of Mark was written first, followed by the Gospel of Matthew and then the author of the Gospel of Luke used both Mark and Matthew as source material. This was advocated by English biblical scholars including Austin Farrer, who wrote On Dispensing With Q in 1955, and by other scholars including Michael Golder and Mark Goodacre. This theory has become more popular over time. The Farrer theory has the advantage of simplicity, as there is no need for hypothetical source “Q” to be created by academics. Advocates of the Farrer theory provide some arguments that Luke used both the previous gospels (Mark and Matthew) but this evidence can be explained by a Matthean Posteriority view. For more information on how the Matthean Posteriority hypothesis is a better fit of the evidence than the Farrer Hypothesis, see the article Matthean Posteriority &; Matthew’s use of Luke as well as Robert MacEwen’s book Matthean Posteriority: An Exploration of Matthew’s Use of Mark and Luke as a Solution to the Synoptic Problem, (London : Bloomsburry T & T Clark (2015))
The insistence on a missing source “Q” stems largely from an assumption that the author of Luke would not have excluded so much of Matthew if he had access to it as a source. However, the author of Luke recognized that there were many narratives before him. His prologue suggests the need, based on his close review of the witnesses, to provide an orderly account for the purposes of providing certainty about the things taught. This implies that Luke excludes much of Matthean material because Matthew largely got things wrong. Another objection to the Farrer Theory is that Luke is more abbreviated in some passages than Matthew and therefore Luke reflects a more primitive text. The author of Luke expresses this motivation in his prologue:
|Luke 1:1-4 (ESV)||1 Inasmuch as many have undertaken to compile a narrative of the things that have been accomplished among us, 2 just as those who from the beginning were eyewitnesses and ministers of the word have delivered them to us, 3 it seemed good to me also, having followed all things closely for some time past, to write an orderly account for you, most excellent Theophilus, 4 that you may have certainty concerning the things you have been taught.|
If one maintains the Farrer theory, this implies that Luke excludes much of Matthew because Matthew largely got things wrong. Accordingly, Luke intends to provide a concise and orderly account, and so he edited out “the fluff” from the passages in Matthew based on what he believed was the most creditable and substantiated attestation of the evidence within his possession. Again, The Farrer Hypothesis maintains that the author of Luke had a copy of Matthew when writing Luke. The implication is that the material in Matthew must have deviated from the sound testimony of eyewitnesses and ministers of the word and that some of the material omitted from Matthew is questionable.
 Gundry, R.H. (1994). Matthew: A Commentary on His Handbook for a Mixed Church under Persecution (Second Edition). Grand Rapids, MI: William B Eerdmans Publishing Company
 Austin M. Farrer, On Dispensing with Q, in D. E. Nineham (ed.), Studies in the Gospels: Essays in Memory of R. H. Lightfoot, Oxford: Blackwell, 1955, pp. 55-88,
 Wikipedia contributors, “Farrer hypothesis,” Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/w/index.php?title=Farrer_hypothesis&oldid=980915501 (accessed October 9, 2020).