First, capitalism is a bad word. Invented by a socialist who intended to insult. A better word to describe the capitalistic society should be "liberalism" where workers have much more freedom in choosing their working relationship, unlike feudalism where they had no right for free movement and slavery where they even had no right to their own lives. The latter two terms describe common workers' working relationship. Yet, the word "capitalism" speaks nothing about it.
Second, fascism spawned from socialism, not capitalism. Mussolini was a socialist and was a part of socialism movement. It was the Soviet's propaganda after WWII that tried to paint fascism as capitalism. Both fascism and socialism are collectivism. Fascism gives a facade of private ownership but takes away the control of the private properties, which is the essence of private ownership. In fascistic society, government runs all businesses, regardless they are called private or public. Government gives production quota and production plans. "Private" owners only get a token of "profit".
Fascism was a compromise that socialists made in an environment in which many socialists had lost faith in Marx' prediction on the collapse of capitalism. They wanted to establish socialism through a path on which they believed to trigger the least resistance from capitalists.