The most important reason why Wilson’s opponents argued against the League of Nations was because America wanted to have an isolationist policy.
After World War I ended in 1918, America wanted to adopt an isolationist policy, that had been previously interrupted due to the war. The U.S. wanted to stay out of global affairs, avoid political or economic alliances that didn't serve their interests and focus on domestic issues instead. Entering the League of Nations, an organization for international cooperation, would mean to be part of international issues, make alliance and defend other nations if it was necessary, among others.
