Final answer:
Wilson's opponents, particularly led by Senator Henry Cabot Lodge, argued against the League of Nations due to fears of compromising U.S. sovereignty and being drawn into European conflicts without congressional consent.
Step-by-step explanation:
The most significant reason why President Wilson's opponents argued against the League of Nations was the concern over sovereign powers and the potential for entangling the United States in European conflicts. Senator Henry Cabot Lodge led the conservative opposition, fearing that Article X of the Treaty of Versailles would mandate the U.S. to engage in military actions for collective security, thereby compromising the country's autonomy in deciding whether to enter a war. These concerns came amidst a broader sentiment of isolationism amongst Senate Republicans who prioritized national sovereignty and the constitutional power of Congress to declare war, over international cooperation.