The Covenant of the League of Nations sought to preserve the political independence and the territorial status quo of member states. However it also demanded that member states disarm to the lowest level consistent with defence and the enforcement of the Covenant.
However well-meaning this sounded on paper, in the real world it was an absurdity. With America declining to join, the most powerful members were France and Britain. So if the Covenant was to be enforced, it would not be the Bolivian army, for example, that could enforce the Covenant but the French Army and the Royal Navy. However even if they had wanted to, France and Britain were not powerful by themselves to enforce the territorial integrity of every member state. France was focusing on repairing its damaged economy and Britain was exhausted and disillusioned by its experience in the Great War.
Paradoxically, in Britain the same people who tended to be League enthusiasts were also strong supporters of disarmament. When they said Britain should disarm and entrust her security to the League they were in reality saying that British security should rest on its weakness. When they said that France should also disarm, they were unwittingly depriving the League of the only land force capable of enforcing the Covenant.
Also, the Covenant's demand that the global territorial status quo be maintained went against the national interests of the most powerful members. For example, Britain and France should have forced Italy to abandon its invasion of Abyssinia according to their obligations under the Covenant. However the existence or non-existence of Abyssinia as an independent state did not infringe on French or British national interests enough to make them launch another war. The Covenant therefore failed to take note of divergent national interests.
Fundamentally, the League had no independent existence of itself. It was a collection of states. It had no armed forces. Thomas Hobbes had said that 'Covenants without swords are but mere words' and his bleak view was borne out by experience. The world was divided by nation states in perpetual struggle with each other. The League had no means by itself to change this international anarchy into a world governed by international law.
Most people would say the primary reason it fell was the United States failure to join and support it. That is just conjecture, the reason it failed was its inability to deal with the aggression by the Axis Powers. The primary purpose of the League of Nations was to "prevent another world war" so when another World War started it had failed its primary purpose.
Additionally the league failed at enforcing article 8 of its charter to reduce "armaments to the lowest point consistent with national safety and the enforcement by common action of international obligations."
There are many other reasons but these are the primary ones.
Walters "A History of the League of Nations"