Because Article 5 ITSELF says that the Falklands fall outside the territory covered by NATO and which would elicit a collective response. https://www.nato.int/cps/en/natolive/official_texts_17120.htm

Art. V:

The Parties agree that an armed attack against one or more of them in Europe or North America shall be considered an attack against them all and consequently they agree that, if such an armed attack occurs, each of them, in exercise of the right of individual or collective self-defence recognised by Article 51 of the Charter of the United Nations, will assist the Party or Parties so attacked by taking forthwith, individually and in concert with the other Parties, such action as it deems necessary, including the use of armed force, to restore and maintain the security of the North Atlantic area. Any such armed attack and all measures taken as a result thereof shall immediately be reported to the Security Council. Such measures shall be terminated when the Security Council has taken the measures necessary to restore and maintain international peace and security .

And to make things more clear this is Article VI:

For the purpose of Article 5, an armed attack on one or more of the Parties is deemed to include an armed attack: •on the territory of any of the Parties in Europe or North America, on the Algerian Departments of France 2, on the territory of Turkey or on the Islands under the jurisdiction of any of the Parties in the North Atlantic area north of the Tropic of Cancer; •on the forces, vessels, or aircraft of any of the Parties, when in or over these territories or any other area in Europe in which occupation forces of any of the Parties were stationed on the date when the Treaty entered into force or the Mediterranean Sea or the North Atlantic area north of the Tropic of Cancer.

The Tropic of Cancer for reference runs basically from between Cuba and Flrida in the Americas and Southern Morocco/Western Sahara in Africa.

When the treaty first came together in the late 40's the old colonial empires of France and Britain were still holding on in many ways. And just as there had been resisitance in some corners, and doubly so in the US to avoid Americans being killed ot protect Europen possessions in the run up to WW2, so was there after. Thus the treay was crafted to trigger a collective response only when the homelands of signatories were threatened not distant colonial holdings such as Vietnam, Malaysia, or the Falklands. But say Bermuda, Gibralter, or the Algerian terriroty considered Metropolitan France were fair game.