It all started with the Lockheed Electra. The Pilots Union got it mandated that the aircraft would be flown with 3 pilots and not 2 pilots and a flight engineer. ALPA also wanted all jet equipment to carry a third pilot.
This was basically a political move to weaken the rival Flight Engineers International Association.
There were a couple of strikes at National and Western Airlines and when they threatened to hire new pilots the new contract was signed, the pilots went back to work and the 3rd pilot issue was put on the back burner.
Boeing built a couple of mock ups for the FAA and ALPA in order to show them the design. ALPA came to the conclusion that 3 pilots were needed and the FAA wrote to Boeing to advise that it tentatively accepted the design.
There was a ballot in the summer of 1967 by United pilots and they voted 92% in favour of a strike if the 737 was not operated by a three pilot crew.
ALPA also proposed at the same time that the BAC1-11 and DC-9 be operated by 3 pilot crews.
The union members instructed ALPA to drop this request and they duly obliged but nonetheless stated that if the 737 was eventually required to operate with 3 crew then they would raise the issue again for the 1-11 and DC-9.
In September 1967 the Air Transport Association of America and the Aerospace Industries Association filed a report with the FAA supporting the two crew position. ALPA disagreed.
During the Thanksgiving week in 1967 the FAA operated a series of flights between Boston and Washington using a pilot from the FAA and one from Boeing. The purpose was to determine workload factors on two crew on the busiest week of the year in America and also in the busiest airspace.
They did two round trips each day for six days. During forty hours of flying they flew in IMC, VMC, carried out below minimum approaches followed by diversions along with simulated instrument failures and simulated pilot incapacitation.
In December 1967 the FAA issued the findings that the aircraft could be operated safely with two crew and would be certified as such.
But it didnt end there. ALPA wasnt happy. Both United and Western had to operate the aircraft with 3 crew members due to union agreements. These were eventually renegotiated over the years and alas the 737 became a two crew airplane.
I hope this goes some way to answering your question.