It is also the consensus position that the evangelist was not the apostle Matthew. Such an idea is based on the second century statements of Papias and Irenaeus. As quoted by Eusebius in Hist. Eccl. 3.39, Papias states: "Matthew put together the oracles [of the Lord] in the Hebrew language, and each one interpreted them as best he could." In Adv. Haer. 3.1.1, Irenaeus says: "Matthew also issued a written Gospel among the Hebrews in their own dialect while Peter and Paul were preaching at Rome and laying the foundations of the church." We know that Irenaeus had read Papias, and it is most likely that Irenaeus was guided by the statement he found there. That statement in Papias itself is considered to be unfounded because the Gospel of Matthew was written in Greek and relied largely upon Mark, not the author's first-hand experience.
Herman N. Ridderbos writes (Matthew, p. 7):
This means, however, that we can no longer accept the traditional view of Matthew's authorship. At least two things forbid us to do so. First, the tradition maintains that Matthew authored an Aramaic writing, while the standpoint I have adopted does not allow us to regard our Greek text as a translation of an Aramaic original. Second, it is extremely doubtful that an eyewitness like the apostle Matthew would have made such extensive use of material as a comparison of the two Gospels indicates. Mark, after all, did not even belong to the circle of the apostles. Indeed Matthew's Gospel surpasses those of the other synoptic writers neither in vividness of presentation nor in detail, as we would expect in an eyewitness report, yet neither Mark nor Luke had been among those who had followed Jesus from the beginning of His public ministry.
J. C. Fenton argues (The Gospel of Saint Matthew, p. 12):
It is usually thought that Mark's Gospel was written about A.D. 65 and that the author of it was neither one of the apostles nor an eyewitness of the majority of the events recorded in his Gospel. Matthew was therefore dependent on the writing of such a man for the production of his book. What Matthew has done, in fact, is to produce a second and enlarged edition of Mark. Moreover, the changes which he makes in Mark's way of telling the story are not those corrections which an eyewitness might make in the account of one who was not an eyewitness. Thus, whereas in Mark's Gospel we may be only one remove from eyewitnesses, in Matthew's Gospel we are at one remove further still.
Francis Write Beare notes (The Gospel according to Matthew, p. 7):
But the dependence of the book upon documentary sources is so great as to forbid us to look upon it as the work of any immediate disciple of Jesus. Apart from that, there are clear indications that it is a product of the second or third Christian generation. The traditional name of Matthew is retained in modern discussion only for convenience.
The author is an anonymous Jewish-Christian. Eduard Schweizer writes (The Good News according to Matthew, p. 16):
The Jewish background is plain. Jewish customs are familiar to everyone (see the discussion of 15:5), the debate about the law is a central question (see the discussion of 5:17-20), and the Sabbath is still observed (see the discussion of 24:20). The dispute with the Pharisees serves primarily as a warning to the community (see the introduction to chapters 24-25); but a reference to leading representatives of the Synagogue is not far below the surface. Above all, the method of learned interpretation of the Law, which "looses" and "binds," was still central for Matthew and his community (see the discussion of 16:19; 18:18). Preservation of sayings, such as 23:2-3, which support the continued authority of...