Although the president has the authority to conduct international treaty negotiations, it is up to the Senate to ratify them. When it came to the Treaty of Versaille, the vehement objections in the Senate meant that the United States never became a party to this peace treaty.
There were two main opposition camps in the Senate. The so-called "Reservationists", led by Henry Cabot Lodge, wanted certain conditions met before they would sign on to the treaty. There were also the "Irreconcilables", who rejected the treaty in any manifestation. Both groups took issue with article 10, which pledged mutual military support if the soverignty of a fellow member of the League of Nations was threatened. They feared that such an international alliance could drag the country into a war that otherwise would not affect it. Indeed, it was mutual military alliances that were largely responsible for WWI to begin with.
They also did not like the idea that United States soldiers could potentially serve under the command of non-Americans if such an event were to occur. Many senators felt that the League of Nations was more of a threat to American interests than otherwise. Lodge considered the League to be a supranational entity that would subordinate the needs of the United States.