Why destroyers were not armored like battleships

Why do people treat unarmored destroyers as a post-World War II development?

Destroyers generally never carried battleship-style armor; modern confusion often comes from inaccurately calling large surface combatants battleships.

Destroyers were designed around speed, weapons, and screening duties rather than battleship protection. Most therefore never carried the armor scheme expected of a capital ship. Loose press usage of the word battleship encourages misleading comparisons with modern destroyers. This distinction separates a long-running destroyer design tradeoff from a supposedly postwar change.