Why was the united states not a member of league of nations

I believe that one main reason why is 1. Woodrow Wilson (Who was a democrat) he believed that he did not need to bring anyone from the Senate, which was a Republican :) (I hope this helps! I read this from the internet, I was gonna post it to you but I dont know if its against the rules of :) If not let me know, and ill send the link)

By signing the Treaty of Versailles, the treaty that set up the League of Nations, that meant agreeing to defend other countries.
Americans did not want to risk more Americans dying in a European war, as they had in World War I.