That's simplistic and only half right. What follows is paraphrased from the book Manual of Political Science (Hague/Harrop).
The origins of the terms left and right date back to revolutionary France, where the pro-monarchy noblemen sat to the right of the president, while the radicals and commoners sat to the left.
Sitting on the right meant supporting the interests of the aristocracy, monarchy and church. Sitting on the left meant being in favour of a secular republic and civil rights.
Because left and right are not words which denote a meaning fixed for once and for all, but rather evolve according to time, space and situation, it's difficult to provide a fixed definition, however we are able to outline some common characteristics in the policies of left and right wing parties in 50 democratic countries post WW2:
Left - peace, internationalism, democracy, public planning and intervention in the economy, commercial safeguards, social security, education, trade unions
Right - support for armed forces, authority and morality, free market, free commerce, law and order, social harmony around a traditional national lifestyle, freedom
As has been mentioned on here before the spectrum of left and right is often portrayed as a horseshoe, because the extreme left and the extreme right have some characteristics in common. But they are not the same, hence they keep fighting each other.
Mussolini was famously a member of the Italian socialist party in the early 20th century, and when in power he enacted certain policies in favour of the poor.
But it's also true that he was also removed from the socialist party for his views, and the majority of his other policies were pro monarchy, strongly discriminatory towards women, not to mention some of his more famous policies.
The extreme left and extreme right have in common 1 - their authoritarianism and 2 - some aspects of their economic policy, and that's about all. It doesn't make them the same.