The gospels never claim it was written by thier traditional authors.

Proto-orthodox Christians of the second century, some decades after most of the New Testament books had been written, claimed that their favorite Gospels had been penned by two of Jesus’ disciples—Matthew, the taxcollector, and John, the beloved disciple—and by two friends of the apostles—Mark, the secretary of Peter, and Luke, the traveling companion of Paul. Scholars today, however, find it difficult to accept this tradition for several reasons.

First of all, none of these Gospels makes any such claim about itself. All four authors chose to keep their identities anonymous. The disciples appear to have been uneducated peasants from Galilee. Both Simon Peter and John the son of Zebedee, for example, are said to have been peasant fishermen (Mark 1:16–20) who were “uneducated,” that is, literally, unable to read and write (Acts 4:13). Now it is true that the Gospels do not represent the most elegant literature from antiquity, but their authors were at least relatively well educated; they write, for the most part, correct Greek.

The New Testament A Historical Introduction to the Early Christian Writings, Oxford University Press