If Matthew was an eyewitness to the events of the life of Jesus, why did Matthew then base his gospel off Mark's?
I'll offer an answer 2 ways--although I do not hold the view that Matthew copied Mark, it is a very common viewpoint.
First I'll evaluate the question as stated. Second, I'll offer an alternate explanation of the evidence. Both approaches will offer an answer the question, though in very different ways.
1. Matthew quoted Mark
Papias of Hieropolis preserved in his history (written ~105) the testimony of a first-generation Christian Elder, indicating that Mark wrote a Gospel based on the preaching of Peter. Clement of Alexandria recorded this information a century later as well. Since Clement provides a number of details not found in any known fragment of Papias (and since Clement was from the Alexandrian church Mark is said to have founded), it is likely that Clement has at least some independent information (For the testimony of Papias, see HE 3.39; for several of the key statements by Clement see HE 2.15 & HE 6.14).
If the Gospel of Mark was based on Peter's preaching, and Matthew considered it reliable and reasonably well-stated, why reinvent the wheel? Peter would seem an excellent source from which Matthew could derive a portion of his material.
Matthew, writing to a Jewish audience, would have rewritten some of what Mark wrote (to Romans), but the core of Mark's Gospel would work just fine as the foundation from which to start.
To use a modern example, it is not unheard of for an eyewitness to an event to quote a statement about the event that was recorded by a journalist. If the journalist did good research and said it well--even if the journalist was not an eyewitness--why not quote their work?
2. Matthew did not quote Mark
I say this knowing full well I'm fighting against the current. Markan Priority (the view that Mark was the first of the Synoptic Gospels written) has been very popular in New Testament scholarship since the 1870s in German and the 1920s in English. I offer a critique of the major arguments for Markan Priority on this site here, and an extensive critique on my YouTube channel here.
I do not believe that Matthew's Gospel is based on Mark's, but that Mark's Gospel was based on Matthew's. If Mark did not precede Matthew, the answer to the OP's question would be a simple: he didn't.
Frank Luke offers an excellent summary of the case for Matthean Priority (that Matthew was the first of the Synoptic Gospels) on this site here.
My principal arguments for Matthean Priority are:
- The Argument from Order -- Mark's ordering of the material is sensible if Mark wrote 3rd. Matthew or Luke's order is implausible if either of them wrote third. My thoughts here.
- The Patristic Testimony -- the early Christian historians are unanimous in their testimony that Matthew wrote first. My thoughts here.
- The fact that the Jewish Gospel of Matthew was the most popular Gospel in the early Gentile church. This is sensible if Matthew was considered the primary source. This is difficult to rationalize if the Gospel that calls Gentiles "dogs" upstaged a Gentile Gospel (Mark or Luke) and was written by a Jewish Christian during the time period in which Judaism & Christianity went through their final, painful separation. My thoughts here.
Why did Matthew quote Mark? I believe it is possible to argue for why an eyewitness would use another's work if he considered the work well-done. I believe it is even easier to answer the question by saying Matthew didn't quote Mark.
Matthew and Luke seem to build upon the shorter Gospel of Mark. What would make sense is Matthew had a Hebrew/Aramaic gospel before Mark. Quoting Irenaeus:
Matthew also issued a written Gospel among the Hebrews in their own dialect,...
If Mark translated much of Matthew's Hebrew/Aramaic gospel, then then it would make sense that Matthew used that translation when later writing his gospel in Greek that we have now.
THEORIES From Keown, M. J. (2018). Discovering the New Testament: An Introduction to Its Background, Theology, and Themes: The Gospels & Acts (Vol. I). Bellingham, WA: Lexham Press.
Based on Oral Tradition
This perspective was elaborated by J. Geiseler (1818), was popular in the nineteenth century, and retains support today from John M. Rist and Bo Reicke. As in the case of the previous theory, this does not account for the similarities in detail concerning wording, sentence structure, and order found in the three Gospels. (p. 112)
This theory sees the differences between the Gospels coming from the different handling of the common original Aramaic or Hebrew Gospel. This was first proposed by German scholar G. E. Lessing in 1771 and was developed by others including J. Eichhorn, who argued for several lost gospels as the original sources for the Synoptic Gospels. This did not find favor apart from C. C. Torrey in 1933.9 Another similar view is that of F. Schleiermacher, who argues that several fragments of gospel tradition existed in the early church and formed the basis for the Gospels. However, this does not account for the high degree of similarity in wording and order, which requires literary dependence. (p. 113)
The Augustinian or Griesbach Hypothesis (p. 114)
Augustinian & Griesbach are separate hypotheses. Augustinian has Matthew > Mark > Luke. Griesbach has Matthew > Luke > Mark. In both cases the 2nd Gospel depended on the 1st, and the 3rd depended on both of the previous
Few scholars accept this understanding today, although William Farmer has supported it in the twentieth century. (p. 114)
Markan Priority, Q, and the Two- or Four-Source Hypothesis (p. 115)
From 19th century, basically Matt. and Luke depended on Mark and Q. Four-source has Matt. and Luke also having their own sources.
Farrer or Farrer-Goulder Hypothesis (p. 117)
Rejected Q based on no evidence. 1st Mark, then Matt. depended on Mark; Luke depended on other two.
Wilke Hypothesis (p. 118)
1st Mark, the Luke depended on Mark; Matt. depended on other two.
I'll stop here. It goes on with followed by a conclusion and M. J. Keown's theory, which does include Matthew's Hebrew/Aramaic gospel.