"In Europe, especially, the connotations [of 'Left' and 'Right'] were extensive and very rich. The 'man of the Left' liked a plain suit of clothes, and the farther left the plainer and simpler until you reached the soft collar and cap and loose flowing tie of the Bohemian rebel. The man of the Right liked titles and ceremonies; he addressed people with careful regard for the distance between them. He revered personages and looked down on mere human beings. The man of the Left shook hands and said hello to everybody, and why not? The man of the Right was for law and order as good in themselves. The man of the Left was for law primarily as a defense of the rights of hthe citizen and his liberties. The man of the Right was conventional and inclined to respect accepted opinions. The man of hte Left was ready to kick over the conventions, and go in for independent inquiry on any subject. All these traits enriched the connotation of left and right, but most of all, and at the bottom of all, the attitude toward the constituted authorities, to the state: 'the individual on one side, the state on the other, that is the underlying substance of this contrast,' says J. Pera in an engaging essay on this subject [Etudes Materialistes, No. 14, September, 1947].
"Now it is clear that not only in their underlying substance, but in all their essential implications, these words left and right have exactly changed places. In America, and I think in all Western countries, a 'leftist' is a man unhorrified by the Soviet tyranny and acquiescent in the gigantic overgrowth of hte state at home. The restauration in Russia of epaulettes, salutes, emblems, and attitudes of rank, the transformation of 'comrade Stalin' first into 'Marshal' and then 'Generalissimo'--even the adoption of the goosestep in the Red Army--did not disturb his feelings. The reverence for a personage passing almost into obeisance before a god was not revolting to him. He accepted, of found excuses for, a system of law which, instead of defending men's liberties, was focused upon suppressing them, and where it failed of that could be replaced by administrative decrees, or mere decisions of the state police. Conventions made rigid, opinions handed down by infallible authorities, value judgments made obligatory in every field of endeavor, a fixed hierarchy of caste and imposed status in civil and industial as well as military and political life--all these things were meekly swallowed down. In short, every judgment and choice, every trait and mode of behavior, that once had given meaning tot he word 'right' is now supported or condoned by those whom all agree in calling 'left' or 'leftist."
--Max Eastman, Reflections on the Failure of Socialism, (New York: Devin Adair, 1955), pp. 70-71.
Right-wing as an expression goes back to the States General of the French Revolution of 1789. The traditionalists, upholders of King and Church, sat on the right. This ideology was essentially a development from the absolutist monarchs of the early modern period. The rebels, the worshippers of Voltaire and (especially) Rousseau, sat on the left. These were the only two ideologies at play on the European continent at the time.
The problem is that these two ideologies just weren’t involved in the American Revolution or the early American experience. The American Revolution was fought and won by believers in the British Whig ideology, which was quite different from either of the two contending European ideologies. To over-simplify, it was descended from the aristocratic opponents of an absolutist King, Magna Carta, the Roundheads and all that. The ideology died on the Continent because the constant foreign warfare indulged in by Europeans required a single decision maker, as warfare always does. Poland, for example, tried to hold onto the ideal of “aristocratic freedom,” and was absorbed by its neighbors as a result. Britain, alone on an island, didn’t face this dilemma, and the ideology was able to survive and thrive.
Originally, the “free men” it stood up for were basically the nobles. Over time, this category expanded. By the time of the American Revolution, or shortly thereafter, it meant all white men. It later expanded further to include all adults.
After the American Revolution, the American political spectrum ran from conservative Whig (Burke/Hamilton/Washington/Federalist) to liberal Whig (Charles James Fox/Jefferson/Madison/Republican). There were no upholders of an absolutist King and state Church, or of the “general will” promoted by Rousseau. This split continued down to the rise of the Progressive Movement in the late 19th century, which was an import of European socialist left-wing ideas foreign to the American experience to that point.
The ideals of the American Revolution, which is what American conservatives want to conserve, thus had essentially nothing to do with either the right wing or the left wing of the French Revolution. So the term is inappropriate.
However, American “liberals” have abandoned even a facade of upholding American revolutionary ideals and have become European socialists and thus are in direct line of descent from the left wing of the French Revolution.