Boeing faced an unthinkable defection in the spring of 2011. American Airlines, an exclusive Boeing customer for more than a decade, was ready to place an order for hundreds of new, fuel-efficient jets from the world’s other major aircraft manufacturer, Airbus.

The chief executive of American called Boeing’s leader, W. James McNerney Jr., to say a deal was close. If Boeing wanted the business, it would need to move aggressively, the airline executive, Gerard Arpey, told Mr. McNerney.

To win over American, Boeing ditched the idea of developing a new passenger plane, which would take a decade. Instead, it decided to update its workhorse 737, promising the plane would be done in six years.

The 737 Max was born roughly three months later.

The competitive pressure to build the jet — which permeated the entire design and development — now threatens the reputation and profits of Boeing, after two deadly crashes of the 737 Max in less than five months. Prosecutors and regulators are investigating whether the effort to design, produce and certify the Max was rushed, leading Boeing to miss crucial safety risks and to underplay the need for pilot training.