The League of Nations was notably started by Woodrow Wilson, shortly after World War I. The main goal of the League of Nations was to prevent another war and keep the peace between the nations.
Although the League of Nations sounded like an amazing idea, it was ultimately a failure and did not end up working as planned in the end. The League of Nations were very weak and had no power to actually do anything, they could not enforce peace and didn't even have any troops to help. It was also very slow, often taking months to make decisions and when made had no power to act on them.
The debate you are talking about was another aspect that lead to the League of Nations downfall. The American public <em>did not </em>want to join for multiple reasons. The Americans<em> did not</em> believe in the League of Nations and would much rather keep out of European occurrences, so America never joined the League of Nations, which made it suffer.
Eventually, the League of Nations was no longer, as people felt it was useless and held no real power, although it was a good idea to begin with.