Why 3-inch guns offered a useful anti-aircraft compromise

Why might a navy prefer 3-inch anti-aircraft guns to 100 mm weapons?

They were lighter and quicker to train, retained much of a 4-inch gun's destructive effect, and hit harder than 40 mm weapons.

The exchange compares 100 mm and 76 mm anti-aircraft weapons without treating calibre alone as decisive. A 3-inch gun could approach the larger weapon's useful rate and destructive effect while remaining lighter and easier to train. At the same time, it struck harder than a 40 mm gun without surrendering all of the lighter weapon's volume of fire. The result was a practical middle layer for ships trying to balance heavy and close-range air defence.