Why is it that we use the physical layout of the French revolutionary assembly to define the political divisions in most countries today? The political terms "right" and "left" originated in the fact that the supporters of the monarchy sat to the right of the assembly president and those who supported the revolution to the president's left. They ceased to have much relevance even in France as the monarchy was abolished and the revolution fractured into factions that settled their internecine scores with the guillotine.
Wikipedia, that ultimate source of fake news, would have you believe that the modern left represents "ideas such as freedom, equality, fraternity, rights, progress, reform and internationalism", whereas the right represents "notions such as authority, hierarchy, order, duty, tradition, reaction and nationalism". You need to read no further than the use of the term "ideas" to describe the left and the more derogatory "notions" for the right to know the political sympathies of those who edited the article. It is so biased you could be forgiven for thinking it first appeared in The Onion or Babylon Bee. One thing the Wikipedia article does get right is that it lists libertarianism on both sides of the left-right divide, which suggests that even the lefties who dominate Wikipedia editing realise that libertarianism doesn't fit the dichotomy.
The respectability of the left and the vilification of the right in the West today is inconsistent and highly hypocritical. The extreme left, in the form of Marxist-Leninism, Maoism, and other forms of Communism, has been responsible for far more human misery and deaths in the last century than the extreme right, and they are indistinguishable in their means and ends. The Chinese Communist Party today, for example, fits Wikipedia's definition of Fascism precisely: dictatorial power, forcible suppression of opposition, as well as strong regimentation of society and of the economy. The only real point of difference between Fascism and Communism in practice is that the former tolerates private ownership so long as it serves the purposes of the state - and this is also true of the Chinese political system today. Both Hitler and Mussolini saw themselves as socialists, and the left's casting of them at the opposite end of the political spectrum is a very successful piece of historic revisionism.
The real philosophical antipodes are totalitarianism and freedom, with extreme right and extreme left on the totalitarian end of the spectrum. Both are about using human characteristics to categorise people into groups that are set in opposition to one another. The extreme right uses nationality and race, whereas the extreme left has traditionally used class - but now also race, sex or gender, and sexuality. It's classic divide-and-rule and scapegoat tactics. Blaming the "other" for one group's misfortunes is the despot's oldest trick, whether it is the Nazis vilifying the Jews for Germany's misfortunes following World War One or Black Lives Matter blaming white people for the situation of African-Americans today.
The true contemporary Fascists are Antifa. You only need to look at them in their black outfits and masks, carrying weapons and beating up innocent people on the streets, to appreciate the parallels with Mussolini's blackshirts or Hitler's Brownshirts. The smashing and looting of businesses is a mirror of the events of Kristallnacht. The Black Lives Matter protestors who recently marched in cities all over the world are their "useful idiots", having been co-opted to their cause but perhaps not fully understanding what they are supporting.
The true liberals (in the classical sense of the word rather than the perverted American appropriation of it) are libertarians like me, who believe in individual rights and maximum freedom in all spheres of life - political, social and economic. We understand that you cannot have a big state proscribing freedom in one area without it affecting every other area of life. The desire of the left to have maximum freedom in the social sphere, such as the freedom to marry whoever you want, is incompatible with their desire to have the state dominate the economic sphere. Likewise, the right is contradictory when it (often somewhat selectively) advocates for free markets while trying to limit political or religious freedom.
Libertarians can be defined by their opposition to the use of force in political, social and economic relations. We believe individuals are sovereign and that governments derive their legitimate authority only from the consent of the governed. We believe that the legitimate purpose of government is to protect individual rights and that the role of government should be limited to activities that are consistent with this. That means the state ought not to interfere with who you marry or with whom you trade. It also means we are in opposition with big state advocates on the right or the left.