World War I and its aftermath helped to lead to the rise of fascism in Europe because it led to economic problems, political instability, and unhappiness among people of some of the countries of Europe. This led people to want some sort of government that would keep order and restore stability, which they thought fascism could do. Let us look at the rise of fascism in Italy and Germany to see how this is true.
Italy was on the winning side of WWI, but Italians were still unhappy with the result of the war. They wanted to get more territory as a reward for their participation in the war. In addition, the end of the war brought economic problems. Because of these factors, many people were unhappy with the government which led to a great deal of political upheaval. When fascists promised to restore stability, prosperity, and Italian power, people were happy to support them.
In Germany, people were even less happy after the war. Germany had lost the war and the Treaty of Versailles had treated them very harshly. It had forced them to give up much of their territory, to forego the right to have a real military, and required them to admit the war was their fault and to pay reparations for it. This humiliation, along with the economic problems caused by the onset of the Great Depression, made it so that many Germans wanted a strong government that would fix all of their problems. The Nazis (who were fascists) claimed that they could do this and that led many people to support them.