Blossman-Myer and Burggren (Comp. Biochem. Phys. A, 155, 2010,259-263) found that the cocoon of the silkworm, Bombyx mori, while creating a tough barrier offering mechanical protection to the pupa, imposes no barrier to the diffusion of oxygen or water vapor. In view of its mechanical properties, silk cocoon is an "emperor's new clothes" for pupa. A theoretical analysis is given to explain the fascinating phenomenon by a fractal hydrodynamic model for discontinuous membrane composed of hierarchical silk cascade. The model reveals that when the fractal dimensions of the microstructure of the cocoon meet a special condition, air and water vapor can flow through the cocoon as if there were no cocoon. However, at extremes of weather, the cocoon is an excellent thermal protection for both high and cool temperatures. A better understanding of the cocoon mechanism could help the further design of bio-mimetic artificial clothes for special applications.