What is the necessity of arc management in a circuit breaker?
Arc formation is not necessary in a circuit breaker. It is an undesirable but depending on current carried, unavoidable aspect of circuit breakers.

Arcs are generated when the flow of current is interrupted. A circuit breaker should incorporate a way to contain and extinguish this arc, and keep the device cool while the arc exists.

Hence, a better question might be, "why is arc management necessary in a circuit breaker?"