The main reason why the League of Nations failed is that the major countries of the world were not committed enough to the League to make sure that other countries would take it seriously.
The main purpose of the League of Nations was to keep the peace in the world. The League was set up after WWI to try to make sure that such a war never happened again. Clearly, it failed to accomplish this.
One of the main ways that the League was supposed to keep the peace was through collective defense. If a country was attacked militarily, other countries were supposed to come to its aid to stop the attacker. The problem with this was that the strong countries of the world were not really interested in exerting themselves to help the weak countries. The US was so uninterested in this that it never even joined the League.
Because the US was not in the League and because other powers were not interested in fighting to protect countries that were attacked, the League failed. It did essentially nothing when Italy invaded Ethiopia. It did essentially nothing when Japan invaded China. When the League was unable to prevent these aggressive actions, it was clear that the it had failed because of a lack of commitment on the part of the major countries of the world.