Why didn't Woodrow Wilson join the league of nations?

US President Woodrow was the 28th US president and served from 1913 to 1921. He was both a graduate and a president of Princeton University. Clearly Wilson wanted the US to join the League of Nations. He believed that as a member, the US was not making itself a participant in any future European wars. The reverse, he believed that a US membership could help prevent future world wars. Wilson was awarded the Nobel Peace Prize in 1919 for advocating the creation of the League of Nations. This should make it clear that he favored the US joining the League. He died in 1924 and never saw the clouds of a new war forming.