Communication Breakdown; Situational Awareness
Deviation - Track / Heading All Types; Deviation / Discrepancy - Procedural Clearance; Flight Deck / Cabin / Aircraft Event Other / Unknown
Flight Crew Became Reoriented; Flight Crew Returned To Clearance
Human Factors
We were cleared for take off 12R MMUN were instructed to follow ROTGI one ALFA departure; contact departure control at the departure end of the runway.  Passing through 2;500 we were radar identified and told to turn 'left to heading of 360; intercept the airway' The autopilot was not engaged. I read the clearance back turned the heading selector to 360 and asked the flying pilot; the captain; if he would like that set up in the box?  The Captain engaged the autopilot told me no and called for Flaps 0 after takeoff checklist.  I checked the speed raised the flaps and engaged the right pack and proceeded with the after takeoff checklist.  The Prior to intercept of the airway the captain turned the aircraft left [right?]; away from course. I told him that I thought the course was to his left.  He did not respond but then keyed the mike and informed ATC we are unable to intercept the airway.  ATC responded that we should be able to intercept the airway from the 360 heading.  I again said the course is to the left of us.  ATC then instructed us to contact Merida center.  At this point; I thought the captain was flying this aircraft single pilot and he had a lost look on his face.  I pulled up the airway on the [tablet]; Tuned in CUN VOR; Dialed in the 012 radial and displayed the VOR on my NAV display.  The NAV display confirmed we were to the right of course and tracking away from course. The captain still took no action.  I then told him 'the course is to our left; you see I have the VOR on the NAV display.'   He then told me he didn't understand.  I told him 'the course is to the left; it is the 012 radial from Cancun.'  He then started scrolling through the FMS.  I contacted Merida Center.  Between transmissions I noticed we were still tracking further from course and the captain still failed to take action.  We were VFR and I debated taking control of the aircraft.  I then asked Merida Center for Direct RAKAR.  Merida directed us to fly direct to MYDIA.  The captain then tried to blame me for the error; claiming I did not put it in the box which confused him.  I told him I asked him if he would like it in the FMS and he responded NO.  He then denied it.  I told him we weren't that far off and are now on a direct course.  He continued to try to blame me for not understanding basic airmanship.  He claimed he didn't understand why a course of 012 from Cancun would apply.  He then told me he must not have understood what I was asking and he didn't remember telling me not to insert it into the box.  I explained that the clearance should have been to turn to a 360 heading and intercept M219; which if he looked on his chart is the 012 radial from Cancun.  After several minutes of back and forth; he told me I should have put it in the FMS correctly.  I have 16 years flying jets 121.  Most of my jet time is international heavy experience.  This captain is a VERY challenging individual to fly with.  He routinely ignores clearances and takes over all of the duties without a single warning; removing the other pilot from involvement.  On other legs he would ask for clearances with out asking the flying pilot if it was ok.  HE has ZERO CRM skills and to be honest our CRM classes are lacking.
An A320 First Officer reported a departure from MMUN with the Captain flying; during which a track deviation occurred as the Captain did not comprehend the clearance. The Captain believed that the First Officer had not set up the FMC properly and the First Office felt that the Captain had poor CRM skills.