The idea of seeking to embroil the United States in the affairs of European Nations did not sit well with many in America. Part of the reason why some did not favor Wilson's Fourteen Points was that it severely limited United States options in the matters of Europe. Many of the points that came out of it were nearly impossible to enforce without a demanding role and presence of the United States in the business of Europe. For example, ensuring that there were no more secret alliances between nations would be impossible to enforce unless the United States sacrificed much of its autonomy to the stability of Europe. At the same time, some felt that supporting Wilson's proposals would lose sight of ensuring a sense of domestic tranquility at home as it would make the United States a type of European Watchdog. To a large extent, the United States emerged out of World War I relatively unscathed. In comparison to nations like Russia or Germany who lost so many more civilians and soldiers than the United States, American casualties were far less and some felt that this blessing should not be tested with further involvement in European affairs.
Different leaders would have opposed the 14 Points for different reasons.
For example, most of the American opposition to it was because of the idea of the League of Nations. If America was to become part of such a league (the opponents feared) it would be forced to fight wars to protect countries it did not care about.
Another objection to the 14 Points was because of its overall idealism. People like Theodore Roosevelt did not think that the world could be run in a way that was based on morality. For example, the idea that all these little groups of people should rule themselves went against the idea of having colonies and empire. Many leaders, including Roosevelt, felt that stronger countries should be able to have empires and "spheres of influence" -- things that the 14 Points denounced.
Woodrow Wilson's 14 Points were written to promote freedom and sovereignty for all nations and to create an open dialogue among countries. Wilson 's 14 points were largely ignored for many reasons including the League of Nations which although was established was never accepted by the United States.
The League of Nations was designed to help avoid another war in Europe. The idea that each member country would have an outlet to discuss their differences before they became a global issue was idealistic indeed. The problem most Americans had with the League was that if a member nation went to war then they would all go to war. Congress refused to sign a treaty that essentially guaranteed American participation in another world war. The League of Nations was created and America never signed the Treaty of Versailles because of it.
The League of Nations proved to be a failure in the years leading up to WWII. Americans who were against the creation of the League were wise to be cautious.