Learned about this in Social Studies, way back when: so, while President Woodrow Wilson was the League's primary visionary, the United States remained outside the organization due to a disagreement of constitutional law, fierce political rivalries, and an argument over whether this would or would not impact American sovereignty.
Under the Constitution of the United States, their president has the power to negotiate treaties. However, in order for them to become enacted, the Senate (upper house) must ratify them by a two-thirds majority. By numbers, in 1919, the Republicans held a slim majority in the Senate, meaning that Wilson (who was a Democrat) needed to win over a significant number of political opponents to succeed. His failure to invite any high-ranking Republicans to the peace talks in Paris was seen by many as a deliberate snub.
When debate raged, the biggest deal-breaker was listed as Article X of the League of Nations Covenant. This article required member nations to come to the aid of any other member experiencing external aggression. Senator Henry Cabot Lodge, leader of the opposition, feared that Article X would force the U.S. into "entangling alliances" and foreign wars without a formal declaration of war from Congress (essentially, what started WWI in the first place). They believed it stripped the U.S. of its sovereignty and violated the Constitution's mandate that only Congress can declare war. Also, there was a smaller group of senators, mostly isolationists, who refused to join the League under any circumstances, regardless of amendments. This was because of political lines being drawn.
Wilson and Henry Cabot Lodge intensely disliked each other. Lodge drafted a list of "14 Reservations" (a mockery of Wilson's 14 Points speech) that would limit U.S. obligations to the League. Wilson, the stubborn fool that he was, did not want to compromise. He tried to rally public support by travelling across the country, but (and perhaps it was the exertion) he had a stroke on the way and became partly paralyzed. He ordered the Democrats to not give in to Lodge's demands under any circumstances.
So, with two votes, one in 1919, and the other in 1920, the Senate did not meet the 2/3 majority needed to ratify the treaty either time. Interestingly, it was not from Henry Cabot Lodge that we get the expression "to lodge a complaint", but he used that to the best of his abilities to ruin Wilson's reputation.
https://en.wikipedia.org/wiki/League_of_Nations
https://history.state.gov/milestones/1914-1920/league
https://www.jstor.org/stable/25144432
