Fascism can be seen as a product of Western civilization in many ways. Let us look at two of the most important of these.
First, fascism is an outgrowth of nationalism. Nationalism really arose with the French Revolution. Beginning then, leaders started to use the idea of national solidarity as a way to motivate their people. They no longer appealed to loyalty to a ruler but rather to loyalty to one's country. This became even more important as war became a mass endeavor requiring large armies and the consent, in some way, of the people. Fascism grew out of this idea of national solidarity.
Second, fascism is a reaction to things like the growth of democracy and the spread of Enlightenment thinking. These were ideologies that encouraged people to be rational and to seek scientific truths. A backlash to this arose that emphasized emotions and romanticism. Fascism grew out of this because it emphasizes an emotional attachment to one's nation and to one's leader. This was a reaction against the more sterile and emotionless ideas of the Enlightenment.