Why is Mark not the first gospel? We all know that Mark was the first gospel ever written. Why then is it that when the New Testament was compiled, Mark was not listed as the first book in the New Testament? What are the reasons that the Early Fathers put Matthew first?

If the Early Fathers didn't know Mark was the earliest gospel when they compiled New Testament, surely they could reverse their decision if they knew, couldn't they?
There was no mandate that the gospels should appear in the order they were written once they were gathered into a collection.  This is true of the rest of the New Testament as well.  The order is   


the gospel accounts, 
the history of the early church, 
the letters of Paul 

to churches, 
to people, 

letters by other apostles, and 
prophecy.


So, there are a lot of ways the New Testament could have been organized.  They could have organized all the letters according to when they were written rather than by whom and to whom.  Additionally, once John was written, they could have put that first, since its first statement corresponds to the first statement in the first book of the Old Testament.

Whatever the reason, the date of writing does not appear to be the primary consideration in organizing the books of the New Testament.  

One possible explanation, however, could have been that Matthew seems to present Jesus specifically as the King of the Jews, while Mark presents Jesus as the Son of Man.  The idea that the gospel was for the Jew first and then also to the Gentile could have been the reason why Matthew was placed first.  

I do know that some Jewish people, who do pick up the New Testament, are often shocked to find in the very first verses a link from Jesus to Abraham.  This can shatter some false stereotypes that the New Testament is antisemitic.  In fact, in his book Betrayed, Stan Telchin had this exact reaction.  So, again, that is at least a plausible explanation as to why Matthew is first.