The Brookings Institution has already written your paper for you. < eg > (I’m sure that you will find other sources to form your own opinion, of course.)
Try http://www.brook.edu/gs/ic/ic_hp.htm , then scroll down to Background and The Genesis of the Independent Cousel Statute.
Really short answer: Nixon’s Attorney General, Kleindienst, had resigned to avoid an impression of impropriety due to his friensdship with Nixon as the Watergate investigation had proceded. When Nixon appointed Eliott Richardson, the Senate had pressured him to appoint a “special” prosecutor to handle the Watergate mess without involving the AG. Archibald Cox was named special prosecutor. When Cox got too close to the truth, Nixon ordered Richardson to fire Cox. Richardson resigned in protest and a new “special” prosecutor, Leon Jaworsky, was named. With all the bad publicity about Cox and Richardson, Nixon was unable to fire Jaworsky who eventually got most of the facts out.
At that point, Congrees began mulling over the idea of an Independent Counsel who would not report to the AG. The argument for the Independent Counsel was to avoid a more clever Nixon successor from getting rid of the Cox-type situation without suffering the Richardson embarrassment. The argument against was that it had not been needed under the very crafty Nixon (who hoist himself by his own petard) and would not be needed in the future. Eventually, Congress passed the law that expired last June 30.