Not that I know much about the exact definitions of those two systems, but it seems to me that you could have a left-wing Fascistic setup. What specifically about Fascism prevents such?
It's a matter of legitimately "left-wing" ideology being either explicitly socialist in nature or bearing an identifiable family resemblance to socialism. So I'll again mention something I've spoken of before, namely, the contradictions between fascism and socialism. I usually draw from Umberto Eco's conception of "Eternal Fascism" and Zanden's
Pareto and Fascism Reconsidered to do this.
Firstly, as Zanden puts it,
"[O]bedience, discipline, faith and a religious belief in the cardinal tenets of the Fascist creed are put forth as the supreme values of a perfect Fascist. Individual thinking along creative lines is discouraged. What is wanted is not brains, daring ideas, or speculative faculties, but character pressed in the mold of Fascism." This is not consistent with the socialist principle of elimination of alienation as defined by Marx's
The Economic and Philosophical Manuscripts of 1844. Such elimination necessitates revolutionary class consciousness, which obviously conflicts with
"obedience, discipline, faith, etc." Revolutionary class consciousness is also rather inconsistent with the
"cult of tradition" identified by Eco as an integral tenet of Eternal Fascism.
"[T]here can be no advancement of learning. Truth already has been spelled out once and for all, and we can only keep interpreting its obscure message."
From an insistence on revolutionary class consciousness comes opposition to class itself on the part of the socialist. This is egregiously contradictory to the elitism that constitutes a core tenet of fascism. As Eco writes,
"[e]litism is a typical aspect of any reactionary ideology, insofar as it is fundamentally aristocratic, and aristocratic and militaristic elitism cruelly implies contempt for the weak. Ur-Fascism can only advocate a popular elitism."
Fascism also has a necessarily anti-democratic nature. As Zanden notes,
"the mass of men is created to be governed and not to govern; is created to be led and not to lead, and is created, finally, to be slaves and not masters: slaves of their animal instincts, their physiological needs, their emotions, and their passions." Similarly, Eco writes that
"the Leader, knowing his power was not delegated to him democratically but was conquered by force, also knows that his force is based upon the weakness of the masses; they are so weak as to need and deserve a ruler." This strongly conflicts with the participatory elements of socialism, as it necessitates the collective ownership of the means of production. For instance, the anarchist Noam Chomsky notes that libertarian socialism is
"based on free voluntary participation of people who produce and create, live their lives freely within institutions they control and with limited hierarchical structures, possibly none at all." Other forms of socialism are of course necessarily democratic at the very least, if not libertarian in nature.
Anarchism can be both left and right.
Anarchism was developed as a pre-Marxist form of socialism, and modern anarchists maintain an opposition to the state and capitalism as facets of their general opposition to hierarchical social, political, and economic arrangements. There are of course capitalists who claim to be anarchists, but they're generally regarded as phonies by the more traditional anarchists, who maintain that anarchism requires socialism.
Fascism is definately not far right.
I'll have to disagree with that on the basis of the collusion between state and corporate power and the financial success enjoyed by private corporations in Nazi Germany, for example, who chose to collaborate extensively with the Third Reich. No brand of economic "leftism," whatever your description of it, could tolerate such broad sustainment of private property rights.