How are the US entry into the Great War and its refusal to join the League of Nations connected?
There were a few main reasons why the US entered World War I on the allied side. One was the German use of "Unrestricted Submarine Warfare", where German u-boats sank any and all shipping that might be giving aid to their enemies, including, as it turned out, some American ships and some with civilians on them. Secondly, Germany had sent the Zimmerman Note to Mexico, promising Mexico military aid and support if they would attack the US to regain the territory lost to us in 1848. We intercepted the telegram, and considered it an act of war. Yet another reason was the fact that the Allies were in danger of losing, and the side we had backed with billions in war supplies and arms might actually be defeated. We did not want to deal with a Kaiser Wilhelm-dominated Europe that was hostile to us.
Afterwards, President Wilson went to great lengths to try and obtain a lasting peace. He achieved only four of his Fourteen Points plan for peace, and the Treaty of Versailles was controversial back home in the US Congress. Although Wilson had negotiated and signed the treaty, the Senate never ratified it, meaning there was no legal way we could join the League of Nations. This, among other things, doomed it to eventual failure.
For both realities, I think that protection of American interests played a vital role. In the entry into the war, America felt that its political interests would be threatened by a world where authoritarianism reigned. When President Wilson seeks to make "the world safe for democracy," it is a statement that American political interests are threatened with an outcome that does not support democratic interests. At the same time, America's post- War refusal to join the League of Nations reflects the protection of self interests overriding all other elements. America perceived the problems in Europe as realities that could cause great damage to America and increase commitments to the region at a time when America was looking to leave it. It is for this reason that protection of interests was cited to avoid further conflict, and why Americans failed to actively support the League of Nations.