Markan priority is most popular because it seems to coincide with statements by the earlier church fathers unanimously asserting that Matthews predated both Mark and Luke. (Lea and Black,The New Testament Its Background and message 2003:122)
The arguments for Markan priorty is based on the brevity of Mark, the verbal agreements among the gospels, the order of events, Mark’s arkward and more primitive style, and Mark’s more primitive theology. In contrast the arguments against Markan priorty is based on doubts of the “Q”. Moreover those doubts include a theology of the “Q”, the agreement in order, Doublets in Matthews and Luke, and different placement of the Q material. (Carson and Moo An Introduction to the New Testament 2005: