You have to consider that NATO was established to protect mainly against direct Soviet threat to Europe. It was not intended to protect the constituents from minor conflicts outside of the general area from non-Soviets, such as protecting overseas dependencies from Argentina.

The North Atlantic Treaty, when signed in 1949, was restrictive to the North Atlantic and Europe for several reasons. Although many European members still had large colonial holdings at the time, the United States, for reasons of public perception, of practicality, and of anti-colonial beliefs, did not want the treaty to be used to defend a dying and discredited concept. The treaty was clearly meant to keep the US involved, at least temporarily, in the defense of a weakened Europe from Communism and the Soviet Union. The treaty covering outside Europe would lose that focus. One thing to also look at is the UN Charter, preceded the North Atlantic Treaty by 4 years. Although NATO does not claim to be a regional organization of the United Nations as defined in Article 52 of the Charter, NATO did consider that as a possibility in its early years. In later years, the regional aspect of NATO was a useful counter-propaganda tool. The USSR was constantly vilifying NATO as an imperialist and aggressive group, so NATO worked to prove it was both purely defensive in nature, and limited in its geographic scope.

Specifically to your question of the Falklands: The question on this specific topic may also be procedural. We can't talk about the one time Article 5 was invoked (too recent for subreddit rules), but I can say this: invoking Article 5 would require both the UK to ask for it to be brought up, and for all Allies to unanimously agree that it should be invoked. So during the Falklands, the UK either did not consider NATO a necessary partner in the war, or believed that Article 5 was inappropriate (due to the geographical restriction), or that they would meet opposition from one of the other members who might disagree.