B737-800
Flight Crew Instrument; Flight Crew Air Transport Pilot (ATP); Flight Crew Multiengine
Flight Crew Last 90 Days 535; Flight Crew Type 8000
Confusion; Distraction; Time Pressure
ATC Issue All Types; Conflict Ground Conflict; Critical; Deviation / Discrepancy - Procedural Clearance; Deviation / Discrepancy - Procedural Published Material / Policy; Ground Incursion Taxiway
Air Traffic Control Issued New Clearance; Air Traffic Control Issued Advisory / Alert; Air Traffic Control Separated Traffic; Flight Crew Requested ATC Assistance / Clarification
Company Policy; Human Factors; Procedure
We pushed from [the] gate; started both engines and turned the aircraft around and approached the ramp. The First Officer called Ground Metering. They responded to monitor Ground Control. Ground Control stated to turn right onto Taxiway Charlie and taxi to the runway. Approaching the taxiway hold short line; Ground Control stated hurriedly '(our call sign) hold your position.' Our aircraft was quickly approaching the hold short line and I knew our four Flight Attendants were up in the cabin working hard and quickly to prepare the cabin for departure on this very short taxi. I did NOT slam on the brakes; yet did apply moderate braking to comply with Ground Control's directive. The aircraft was approximately nine feet over the striped line defining the border of the ramp and the taxiway.I keyed the microphone myself; or asked the First Officer to tell Ground Control (I do not remember which) that we were well over the taxiway line. There was a very rapidly approaching Company aircraft who was taxiing southeast on [the] taxiway for departure. Ground Control asked that Company if he could pass in front of us at the intersection. Company aircraft stated 'no problem.' Ground then advised us to hold our position and give way to Company. This was a big problem for us. The late directive from Ground control put us in a very precarious position. We were exposed and I felt we were in a position that could lead to a ground collision. The Company aircraft was traveling at a very high rate of speed and I was very uncomfortable. I knew that nothing was going to stop our Company. It was clear he was intent on somehow maneuvering around us. There was not time to advise ATC of our disagreement and work out 'Plan C.'  Instead of complying with Ground Control's clearance; I turned the aircraft full tiller to the right and initiated a 360 degree turn back onto the ramp; away from the speeding Company aircraft aimed directly at us. As I did so I keyed the microphone and stated 'Ground; we're not going to do that. We're turning to the right and will get in line with Company after our turn.'I stopped the aircraft after our turn and noticed that Company had maintained it's high speed. He was now approaching a left turn at the next taxiway. During the turn; Ground told us to taxi behind Company. I was very concerned and a little upset that ATC would both put us in that position and attempt to clear an aircraft around us when it should have been clear from our statement over Ground that we were well over the taxiway  ramp line. Also at fault was the speeding Company aircraft. I wonder quite often when the pilots of this airline will come to their senses and slow down while taxiing. The action is unsafe; unprofessional and I do not appreciate it. The actions I took were the best I could do in the limited time I had to make a decision. I stand by them.
B737 Captain reported they were unable to stop in a timely manner at a taxiway intersection and then disregarded ATC's subsequent taxi instructions to avoid another aircraft.