Woodrow Wilson, who was President of the USA at the time of the League's creation, was the person who pushed for the inclusion of the League in the Treaty of Versailles in the first place. Why is it that he never managed to convince the American people, and the Senate, to have the USA join the League?
There were quite a few reasons:
With no way to form a significant voting bloc the Treaty of Versailles was rejected by the Senate, and any participation in the League of Nations. Isolationism probably played a part in this as well, considering that America entered a protectionist phase soon after, and really did not want to get involved in WWI in the first place.
Wilson was unusual for his time. In an era when Republicans dominated the U.S. government, he was one of only two Democratic Presidents between James Buchanan (1857) and FDR (1933). (Grover Cleveland was the other.) Wilson was elected in 1912 only because of the "split" between Republicans (Teddy) Roosevelt and Taft, and Wilson barely won re-election in 1916 (277 electoral votes to 254) even as a "sitting" President, running on the slogan, "He kept us out of war."
Americans of the time reveled in their "splendid isolation," and didn't want to take part in "foreign affairs." In his Farewell Address, George Washington had warned "America" against "entangling alliances." Americans of Wilson's time (particularly Republicans) still clung to this idea.