Why battleships carried six-inch secondary guns

Why did capital ships carry six-inch guns along their sides?

They were meant to repel destroyers and light cruisers without using the main battery, although later dual-purpose batteries offered a more efficient solution.

These guns were intended to defeat smaller surface threats without spending scarce main-battery shells. Destroyers and light cruisers could be engaged with a caliber suited to their size while the heaviest guns stayed available for capital targets. The design logic was ammunition economy and layered defence rather than duplication of the main battery. The arrangement made more sense before a single dual-purpose secondary battery could cover surface and air threats efficiently.