To ask the horse to back up is to ask him to go forward.  Sounds like a paradox does it not?  Remembering that the bridle is a tool that blocks unwanted direction, ask the horse to move forward into hands that do not pull back, but block from going forward, left or right.  Have your legs ready to block any sideways movement.  The only “open door” available is to go backward.  Be patient when first teaching your horse to back up.  Only ask for a step or two and then give lots of praise.