The League of Nations was weakened by it because the founder of the League (President Woodrow Wilson) was American, and his own country wouldnt join it. The League's power was called into question, and their military strength was made significantly weaker. Their only peacemaking strategy was through economic sanctions (so they really didn't have much power at all over other nations). Basically, it was because other nations that had played significant roles in the first world war refused to join/weren't allowed to join the League (ex. Germany and Russia) that led to its demise.
Because it was rough time.
