Your confusion is justified. It shouldn’t work, all things equal.

I think it’s because the intake of a plane is more diffuse; it’s pulling air in from different directions. Meanwhile, the “reverse exhaust” is ejected from a smaller nozzle at higher temperature; it has a higher velocity, therefore more momentum to “push” the plane than the intake “pulling” it.

For the record, there’s a similar scheme for sailboats. Hook a fan in the air to a propeller in the water, and the wind imparts less momentum than the prop “pushing” on the water. Such a “rotary sailboat” can sail straight into the wind.