In general, the right tends to think emotionally, while the left tends to think logically. But it varies. Overall, the more left, the more equal. And the more right, the more hierarchy.
Early fascism, which has socialist roots, and which it especially rooted from national syndicalism, is neither left nor right. It was Third Position. It had elements from both the left and the right. Early fascists such as Giovanni Gentile or Filippo Tommaso Marinetti were atheists and futurists. Fascists were progressives that viewed liberal democracy as obsolete and degenerate.
While early and real fascism is Third Position rather than right wing, practically all fascist affiliates since the Second World War are in the right wing because fascists are anti feminists, they promote the family institution, they support classes (class collaboration, the rich for the poor, the poor for the rich), they believe that women should marry their rapists (this was normal in Italy, especially in southern Italy until the 1970's), and fascists believe that many of the personal freedoms that people have today, such as the right to have sex casually, were created by Jews so that "they can rule you."
Collectively, fascism has not been popular since the 1940's. Most "fascist" groups since the 1940's are far right wing, ultranationalist people who are extremely anti communist, anti feminist, and who strongly promote the family institution. Most of these "fascist" groups are rather neo-Nazi, ultranationalist, ultraconservative, extreme monarchist, libertarian capitalist, Christian Fundamentalist, and/or reactionary. Some examples of these "fascist" groups are the American Nazi Party (Nazis don't call themselves Nazis, they call themselves "National Socialists" so you know that the American Nazi Party is not really fascist), Svoboda, the Bosnian Movement of National Pride, the NPD, Golden Dawn, Obóz Narodowo-Radykalny, the Russian National Unity, or the Ku Klux Klan.
The only real fascist that existed after the Second World War was Juan Peron of Argentina. And he was personally friends with revolutionary Che Guevara. One reason being because both of them hated American imperialism.
Fascism and "fascism" usually rises whenever capitalism decays. They use these politics to cope with deteriorating capitalism. Fascist policies and economics are used to conserve the capitalist mode of production. When these ideologies rise, you know that capitalism is phasing off, but these people are using the false conscious politics to handle this. These peoples' genetics and psychologies are a phase behind, rather than forward. Ideas such as national unity, debtless currency, high import taxes, and "saving jobs for the nations' peoples" are tools used to handle decaying capitalism, while still keeping the capitalist mode of production.