Just to follow up long after the fact:
The 19th century German Higher Critics were initially motivated by Antisemitism. They couldn't have a Jewish author as the composer o the first Gospel. So they imagined a Gentile church in the second century writing the four Gospels.
Marcan priority only makes sense if you ASSUME that the Gospels were written long after the fact and that these authors were not eyewitnesses. You have the so-called "synoptic" passages that must have come about by one author copying the text of another and redacting the text to suit his own agenda.
It's funny that the people who hold to the copying theory are the first ones to point out all the alleged "contradictions" in the Gospels. My view is that the Gospels seem to contradict each other (or they present difficulties in places) precisely because they were composed independently of each other
If the Apostles at Jerusalem originated the Gospel in oral form in the 30s and 40s AD, then the Synoptic passages can be explained through a common memorized Gospel that was written down independently, but still has many of the original catch phrases that the Apostles used to preach.
Matthew was written in Jerusalem about 40 AD (or at least a proto-version of Matthew, a Greek version may have been written later); Mark and Luke were written about the same time in 65 or 66 AD; Mark writing in Rome, Italy and Luke writing in Achaea, Greece. Acts was written in the same year as Luke. John was written a few years later from Ephesus, Asia Minor.