Question

why the plasma membrane is flexible while cell wall is rigid

Answer 1

The cell membrane is flexible because of the presence of oil like substances called phospholipids, which gives it a fluid nature. While as the cell walls are rigid because of the presence of the thick layers of the substances like cellulose in plants, chitin in fungi and peptidoglycon in bacteria. The cell wall protects the cell from environmental stress.

Answer 2

Actually cell wall should be rigid as it has to protect plants in all types of weather. Moreover it's made up of cellulose. While cell membrane is made up of the oil like substance called phospolipids which makes it flexible.
Hope it helps u dear