The pressure between the layers of the pleura is negative due to the following reasons:
High-Yield Explanation
The tendency of the lungs and thoracic wall to recoil in the opposite direction expands the intrapleural space and creates negative pressure i.e. below the atmospheric pressure in between the two layers of pleura. Ref: Fundamentals of Respiratory Physiology By A. S. Chakrabay, Chakrabay, 2007, Page 33