Many of those Senators were afraid that membership in the League of Nations would reduce the sovereignty of the United States and it's ability to have complete control over it's own foreign policy and military actions. The treaty creating the League of Nations committed members of the League to defend the independence of any other member that got attacked by another country. Many Senators worried that this would force the US to go to war whenever any member of the League was attacked by another country over it's military and it's foreign policy. So then the Senate decided it would be best, to reject membership in the League of Nations to prevent the US from being forced into a firefight that wasn't their own.