Why couldn't women wear nylons during World War 2?

Nylon stockings in WW2

Nylon stockings first went on sale to the general public in May 1940 and were extremely popular.

However, by 1942 demand for nylon for military use (for example for parachutes) was so great that very few stockings were made. It took till March 1946 for Du Pont to satisfy demand in the U.S.