Final answer:
General Douglas MacArthur's mistake during the Korean War was his call for the use of nuclear weapons against China, and his aggressive actions that risked expanding the conflict, which went against the Truman administration's policy of limiting the war to avoid a larger global confrontation.
Step-by-step explanation:
The mistake that US General Douglas MacArthur made during the Korean War was his insistence on expanding the conflict by using nuclear weapons against China, and his pursuit of an aggressive strategy that risked broadening the war, potentially to include the Soviet Union. MacArthur's determination to extend the war into China and his public disagreement with President Truman on war policies led to his eventual dismissal. General MacArthur greatly underestimated the Chinese commitment to the conflict, as evidenced by his dismissal of warnings from China that its forces would enter the war. His desire to push northward beyond the 38th Parallel and advocacy for the use of nuclear weapons were seen as escalatory and against the principle of limited war, which sought to avoid a larger international conflict.
General MacArthur recommended that President Truman deploy nuclear weapons against China to help win the Korean War. This suggestion, and MacArthur's public criticism of Truman's refusal, demonstrated a severe clash in military and presidential strategy, resulting in MacArthur's relief from command. His recommendation was at odds with the more cautious approach of the Truman administration, which sought to limit the scope of the conflict to avoid a possible World War III scenario with China or the Soviet Union.