This question is wrong, not because the United States will not fight, but because the United States can no longer fight, and it must not sign an armistice agreement. There are several main reasons:
1. Militarily it can't be beaten.
Even though the United States used the most advanced military technology and equipment in the Korean War, including aircraft, tanks, artillery shells, etc., the United States gradually diminished its advantage with the intervention of the Chinese People's Volunteers. In addition, the combat effectiveness and perseverance of the Chinese People's Volunteers exceeded the expectations of the US military, and through three years of fighting, the volunteers became stronger and stronger, and the best were getting better and better, making the decline of the US army on the battlefield irretrievable, and there was no hope of victory.
2. The material cannot be consumed.
Second, the U.S. had a very large consumption in the Korean War, but it did not achieve corresponding results, and its European side also needed a lot of material reconstruction, which was an important reason why the United States decided not to invest more forces.
3. The people can't be deceived.
Thirdly, the defeat of the United States in the Korean War caused Truman to be attacked by the US government and opposition due to a series of social problems caused by the Korean War, thus greatly reducing his reputation among the American public, questioning the justice of the war and demanding withdrawal from the war.
4. Strategically retreated.
Finally, the defeat of the United States in the Korean War forced it to re-examine and change its strategic layout around the world. From the beginning of the Cold War to the end of the Korean War, the US containment policy was mainly manifested in the political and economic aspects, but after the end of the Korean War, the post-war containment policy of the United States shifted from the political and economic level to the military level, and the scope of containment also expanded from Europe to Asia.
To sum up, the United States chose not to continue to invest more forces in the Korean War, mainly because the war was too costly, and its advantages on the battlefield gradually disappeared, and at the same time, the defeat of the United States in the Korean War also had a significant impact on its domestic and foreign image.