Question

Why all protozoa not perform phagocytosis while all of them have cell membrane

Answer 1

it is important to note that a cell needs much more than just a cell membrane in order to perform phagocytosis. it needs some receptors to trigger the operation ,and a large variety of protiens of cells cytoskeleton.

Answer 2

Protozoans are unicellular organisms who use phagocytosis as one of the methods to ingest food. During the process, a portion of their cell membrane surrounds the particle and engulfs it.  

This process is a complex interplay of a large number of triggers, receptors, enzymes and remodelling the cell shape by altering the cytoskeleton.  

While many protozoans use this method for ingesting food, many others who do not have a survival benefit from this process have lost it over time. Hence, all protozoan although have cell membrane do not necessarily perform phagocytosis.