Final answer:
Opponents argued that membership in the League of Nations would involve the US in future world conflicts.
Step-by-step explanation:
U.S. Senators who opposed the nation's participation in the League of Nations argued that membership in the organization would involve the nation in future world conflicts. They believed that being a part of the League of Nations could potentially drag the United States into other countries' disputes and wars. This was a concern after World War I, as many senators wanted to avoid involvement in future conflicts.
Learn more about Opposition to the League of Nations after World War I