What is our evidence that Mark, the companion of Peter, wrote the Gospel of Mark?
The gospel is written somewhere around 65-70 A.D by an author who does not identify himself.
In 125 A.D., a man considered somewhat stupid, wrote that he had heard from unnamed sources that Mark had written down Peter’s teachings in no particular order. This man does not indicate that he had seen the gospel and he does not quote from it.
In 180 A.D. another man identified Mark as the author of the Gospel that now appears under his name in the New Testament. The second man does not indicate his basis for believing that Mark wrote this gospel. He does indicate his basis for believing that there are no more or less than four gospels, which is that there are four winds and cherubim have four faces.
That’s it. That’s our evidence for Markan authorship. We have Papias, who church historian Eusebius considered a man of "very limited understanding," writing a half century after the gospel was written. Papias does not give us any information that would confirm that the book he heard about is the same book that we identify as the Gospel of Mark and in fact gives us some reason to doubt it. Then we have Irenaeous writing a full century after the gospel was written. He does not provide us with his reasons for believing in Markan authorship, but he indicate the types of reasons that he finds convincing when it comes to questions of the authority of the gospels. These reasons do not inspire confidence.
What brings this to mind is Craig Blomberg’s statement in The Case for Christ that the gospel “is obviously based on eyewitness material” and Lee Strobel’s claim that he sought out Blomberg because he was looking for someone who would not make “the kind of sweeping statements that conceal rather than deal with critical issues.”
I don’t think Strobel found his man.