Read my earlier posts. Then think about energy stability, economic stability, nuclear capability, regional influence, capability for the projection of military power into enemy territory, containment of competing ideologies, access to markets, those sorts of assets. We aren't tribals going to war for fertile land and laborers. Think like a modern global civilization and consider who else plays on a global stage. Iran, North Korea, they are currently side shows but let them get nukes, things change. Let the region fall under Russian or Chinese influence unchecked by US interests, things change. Again, we didn't go to war in Korea for kimchee.
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It was, in a vacuum, two dictators fighting over a border drawn by foreign powers (which, of course, is a direct analogy to the recent history of the Middle East). Why did the two superpowers of the Cold War care and each back a horse? Truman's direct quote:
“If we let Korea down, the Soviet will keep right on going and swallow up one piece of Asia after another…If we were to let Asia go, the Near East would collapse and no telling what would happen in Europe.” _ POTUS Truman
"...Truman believed that the Soviets wanted to overrun Iran, gain access to Middle Eastern oil, and find warm-water ports in the Persian Gulf and the Eastern Mediterranean” Source: A Preponderance of Power: National Security, the Truman Administration, and the Cold War
Combat troops had been recalled ahead of the invasion. That removal of combat troops was one reason North Korea decided they could invade. They had the backing of the Soviets and the US wasn't supplying the same level of support to South Korea. Even if we did have a few remaining troops, it would have been much simpler to withdraw them than to hastily reinforce with under-strength and under-equipped divisions, which is what we initially did (well, after resupplying South Korea and some air/naval assets were committed). Both our actions and the words of the decision makers of the time show we didn't go to war because we happened to have some troops there.
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