More people die in a fire because they breathed smoke than people die because they were burned. Because of that, so that people can escape both fire and smoke, they use the narrow stairwell as an escape route. The stairwell has to be free of smoke.
A Stair Pressurization Fan (SPF) uses fresh outside air to increase the air pressure inside the stairway. The increased pressure from the fresh air pushes the building's smoke laden air away from the escape route inside the stairwell. See What is a Stair Pressurization Fan (SPF)?
But there's a problem.
If there's smoke inside the stairwell, turning on the SPF to increase the pressure inside the stairwell pushes the smoke from inside the stairwell into the rest of the building. Pushing smoke into the rest of the building is often worse than not turning on the SPF.
To keep the SPF from pushing smoke into the rest of the building, the smoke detector inside the stairwell doesn't turn on the SPF.