Jesus did not write anything because he lived in a predominant oral society.  The apostles of Jesus followed suit and transmitted the living oral tradition to their disciples and the new followers of Jesus the Christ.  The apostles did not need to write anything, since they could explain everything.  However, once Christianity moved out of Jerusalem there was a need to write things down in a more permanent form.  The early Pauline letters to the new Christian Churches show how Christianity spread.  Increasing time and distance from the place of Jerusalem and the time of Jesus led to a decision to write things down.  In order to prevent heresy or diverse views, while at the same time encouraging the early Christians, the need for a written record became evident.