The Captain and First Officer of a B757-200 miscommunicated with one another in response to a failure of the left engine to light off.

Narrative

I was starting left engine while the Captain was finishing disconnect with ground crew. We had no light-off on L engine. I shut off the fuel cut-off switch per memory item and announced to Captain of no light off on engine start. I broke out card; read item; read reference. The Captain pulled out book and started reading items. She asked me if there was fuel flow; and I answered I wasn't sure at time of switching fuel off; but probably yes since the start seemed normal up to the 20 second point. Captain read along the incorrect set of conditions and instructed me: Fuel Control switch to run. Noticing error; I said that was not it; that we were looking for the no light off condition. At that point I could not understand where she was in the checklist; and she was not offering a clear path. We were approaching five minutes of motoring. With no clear direction and the motor obviously clear of any significant amount of fumes after so much motoring. I announced I was shutting off the starter. I felt we were being drawn into trying to figure out the checklist and ignoring the big motor spinning out there; I felt too distracted to just keep motoring beyond five minutes. I am aware this may have added to her confusion; unfortunately. At that point; the Captain sternly told me to not say anything or do anything and do only what she said. We eventually completed the checklist; although the starter had been disengaged. The three areas of concern we could work on would be CRM; checklist use; and system familiarization. Had I just done what she said without CRM; we would have reintroduced fuel into a faulty-ignition engine.