Why are some enzymes synthesised as inactive precursors?

Many enzymes are produced in as inactive, if there is a potential for causing damage to the cells producing them or to tissues where they are released. Another reason could be if their action requires strict regulation (only activated under specific conditions).

An example of this is 'zymogen' which is an inactive precursor of an enzyme. The pancreas secretes zymogens partly to prevent the enzymes from digesting proteins in the cells in which they are synthesised.

These are then activated later in the duodenum for the digestion of proteins.

Synthesising enzymes as inactive precursors (also called zymogens) can help ensure that the enzymes are only activated when they are needed. A good example of this is in the digestive tract, where you want to control when enzymes like Pepsin are active. Pepsin breaks down protein in discriminately, so you don't want it damaging the chief cells in the stomach lining that are making it. Pepsinogen is the inactive form of the enzyme which is made secreted by the chief cells, the acid in your stomach then activates Pepsinogen turning into its active form Pepsin. This then can start breaking down protein in your food rather than in the cells that have made it.

Enzymes are biological catalysts. They work by forming enzyme substrate complexes to perform reactions. Enzymes perform a variety of reactions, and one of those is degradation/digestion of substrates. An example of such an enzyme is Pepsin in the stomach, which would bind to proteins and break them down. Now, as body's own tissues also contain proteins (Like proteins inside the cell or those on top of cell membrane, like channel and receptor proteins), the Pepsin for digestion is secreted as inactive Pepsinogen so that it does not break down body's own proteins. It only gets activated after it's secreted into the stomach due to low pH of HCl. Another example of such an enzyme is prothrombin, the inactive precursor that plays a role in clotting of blood. Only after it has been converted to active form, thrombin, does it convert fibrinogen to fibrin meshwork, forming a clot. Having the active thrombin floating around in blood plasma would result in spontaneous clot formations.