Why an armoured flight deck can save weight

Why would giving a carrier an armoured flight deck make it lighter rather than heavier?

When the flight deck doubles as the main structural deck, it can replace a separate reinforced deck rather than adding armour to a second one.

A question prompted by the Forrestal class compares a carrier whose hangar deck is the main structural deck with one whose flight deck carries the ship's longitudinal strength. Heavy jet aircraft require a strongly reinforced landing surface even before armour is considered. If the strength deck remains below, the designer effectively builds two very strong decks and accepts the resulting top-weight penalty. Combining structural strength, landing loads, and armour at flight-deck level avoids that duplication and allows armour to hang from the same framework. Ark Royal and later British carriers used this arrangement, and wartime American and British naval architects found their decks stronger than the official British calculations had assumed.