There were many reasons why Concorde stopped flying, these are mentioned below.
There were many complaints from public about the noise Concorde made. The noise was not much from the plane but by the supersonic speed, which produced sound like a thunder or a bang.
The Oil crisis that started in 1970s made it very expensive to operate Concorde, and influenced many to-be operators to reconsider their options.
Unlike many other airlines, Concorde still used many analog instrument. And this was one of the reasons Concorde always flew with a flight engineer in every flight.
The 2000 Crash
The crash of Concorde flight diminished the ambition of its operators.
Costly for Passengers
One Concorde ticket costed around one thousand UK pounds, and nearly double for a First class seat, in 1980s. There were not as many customers as were expected to be received.
Non Eco Friendly
A 100-seater Concorde plane burnt 89,000 liters of fuel in a flight, where as other planes carrying about 400 passengers burnt only 59000 liters of fuel, in the same length flight.