In school, I was taught that fascism was not in fact right wing, but compared to American Government, it was very much left wing. Our history class taught that the Nazi party of Germany had a meeting with the Communist Party of Germany to discuss a number of things starting on what slogans would be and what category they would say they were. Fascists were very much left wing, but they looked like right wing extremists compared to the communists, so they decided to call the communists left wing and call the fascists right wing to avoid confusion.
Fascism is left wing because you cannot own a business or large home if you don't toe the line that the ruling party draws.. If you don't toe the line, they take your business and give it to someone who will. It is far right of either communism or socialism in that it allows private property at all. In socialism the government owns all the business and makes sure that everyone is paid equally, and in communism the gov't owns everything and makes sure that everyone has everything they need.
So fascism is far right of communism but still pretty far left of American conservatism. It's somewhere in the middle.
When considering whether or not fascism is right-wing, it's important to remember the ideals of communism, which is an extreme left-wing ideology.
Communism espouses a government that uses its power to enforce a population without economic classes by having a democratic government control all the means of production and resources to be allocated to the population according to needs. By doing away with economic inequalities, inequalities in other areas, such as class, race,and gender, will be done away with. In this way, the whole world may enjoy total equality with each other. This makes the ideals of communism an extremely inclusive ideology.
Fascism, on the other hand, espouses different ideologies. Fascism uses government power so that those in control of government may dictate to others. The reason for this is because only by having a strong government that mandates unity can a nation be strong enough to act, especially against national enemies. Fascism also holds that the population of their nation is of more importance than the populations of other nations. This makes fascism an extremely exclusive ideology. Fascism also tends to hold that others may be exploited for the benefit of that nation.
Those are the main differences between communism and fascism that characterizes communism as left-wing and fascism as right-wing.
Now, both ideologies are statist. But those two ideologies have different goals in how state power should be used.
Also, when people think "communist" they tend to think of Leninist and Stalinist communism, which is much closer to fascism because they were authoritarian dictators who used government power for their own ends and used it to exploit others. This is why most people who advocate the original ideals of communism - economic equality through a democratic government - often label themselves as socialists, especially democratic socialists, in order to make the distinction clear.