The 737 Max is the perfect example of an aircraft that has evolved to fit the needs of a ever-changing aviation market. This aircraft seems ancient when compared to other aircraft of its caliber, such as the A320neo, a much more modern aircraft.
(Silk Air's 737 Max)
(Scoot's A320 Neo)
(AirAsia's A320 Neo)
Boeing wanted to "redesign" (basically just re-engine) its 737. This was a design they were familiar with and have been producing for over 50 years. Boeing's re-designed 737max was to compete with Airbus's A320neo line of aircraft. The 737max would have a maximum range of over 4000 nautical miles, as compared to around 3000 nautical miles for the older variant 737-800. This was a perfect example of an aircraft being adapted to fit the modern day demands of airliners. Moreover, a big selling point of the 737max was that it was 15% more fuel efficient over its previous variant. This was an attractive proposition, in light of rising fuel/oil prices.
(Silk Air's 737 Max)
However, the real determining factor of why certain airlines, such as American Airlines, chose to select the 737max aircraft over the 'all-new' A320neo was because they already operate a fleet of older 737s. This would save the company millions in training both pilots and engineers, as the airframe of the 737max was very much identical to the fleet of older 737s already in service. Moreover, pilots would not even have to complete training on simulators to be certified on the 737Max, as the "new" aircraft handles almost identically to the older variants. This was Boeing's attempt at killing two birds with one stone, an attempt which failed spectacularly.