Short Answer: The left right spectrum is about social hierarchies both cultural oppression and economic inequality facilitate a social hierarchy:
The left–right political spectrum is a system of classifying political positions characteristic of left-right politics, ideologies and parties with emphasis placed on issues of social equality and social hierarchy.
Much Longer Answer:
"Left" and "right" are an antonym pair and as such suitable to describe a spectrum of ideas between two polar opposites. And it's origin is afaik in the French Revolution where in the national assembly people with similar ideas, interests and alignments grouped together creating a sitting order where the revolutionaries sat left and the monarchists sat right.
So yeah there is some arbitrariness in terms of these distinctions and different people looking at it see different spectra idk. Republicans vs monarchists, progressives vs conservatives, libertarians vs authoritarians, equality vs hierarchy, ...
But the French Revolution wasn't just an insurrection it came about in an era where there was a clash between systems. On the one hand you had the Ancien Régime and their feudal caste system and on the other hand you had for almost a century people philosophizing over very different ideas nowadays being called the "Age of Enlightenment".
So the narrative of the god given estate system was under attack from many angles: philosophically, people arguing over social contracts, restricting the absolute monarchs with constitutions, ideas about equality and challenging the social hierarchy, calls for emancipation (nowadays often associated with feminism but technically just the act of demanding one's agency and ending a tutelage) and pretty important: science providing alternative reasoning for how things work and threatening the monopoly of reason held by the church, which served as the legitimization of power (which is why many leftists argue for a "separation of church and state" (in the sense of keeping the church out of the state) because it's pretty hard to have a rational argument against god... or more realistically someone who claims to speak for him/her), while economically constant wars and a lavish lifestyle had bankrupted the country and made a middle class comparatively wealthy while denying them social and political participation and lastly even militarily as with the U.S. revolution and the French revolution the idea of just suppressing those ideas with force was no longer a safe bet.
So a long period of stagnation and snail-like incremental progress was followed suddenly by a period of "rapid" change and "almost anything goes". Like apparently initially people just demanded a constitution to limit the power of the king, but then the king or rather his entourage tried to flee and plot against the revolution and so they were executed one went from reforming a monarchy to abolishing it and establishing a republic (no king necessary at all).
For some "freedom" and "equality" were already realized with the abolition of the caste system and a rule of law that doesn't discriminate. While others probably felt a little underwhelmed by the "massive change". Like what's the point of the rule of law if you're a slave in the U.S. and the rule of law doesn't grant you any rights, but only serves as legitimization to restrict your freedom. Or what if you had the wrong reproductive organs and where technically seen as human but equal rights were still a few hundred years into the future? Just to name two groups for whom "equality" this whole grandstanding talk about freedom and equality might have sounded awesome but who might have thought what they actually got served was more or a joke. I mean that's hypothetical cause in the worst case they wouldn't even have heard the grandstanding talk directly, as they weren't the target audience.
Or what about the peasantry, poor and working class who were told that they are now free and equal citizens of the republic. And when hypothetically asked what changes because of that, got to experience that it was very little. They still had to work for someone else because they didn't own stuff. Just not because of feudal loyalty but due to employments and if they worked long hours their ability to politically participate might have also been more of a theoretical one.
So on the one hand you had a middle class for whom their higher than average income was their route to emancipation and who held that as pretty important. While you still had a lower class for whom that economic inequality was what kept them in servitude just of a different kind. So their "individual and economic freedom" was at best a purely theoretical.
Also "the state" became a more ambivalent role. Previously the state was simple, it was the repressive power structure that, for better or worse, kept things the way they were. But now you had, at least theoretically, democracy and a republic with equality among citizens, so "the state" is different. It's no longer an external repressive power structure (at least if you're part of a majority group and even then more in a theoretical sense), but you're part of that system. You're both oppressor and oppressed.
So you could reject this power and this monopoly of violence, because let's be real the state never abolished violence it just organized it, the police and military is allowed to do it (theoretically with strong restrictions and oversight) and apart from immediate self-defense, no one else. So do you make laws and rule over people with their enforcement or do you put that in the hand of the people and only accept a consensus and trust that people uphold what they decided themselves.
So the role of the state is ambivalent it can be used as a tool for change and for conservation and on a meta level the power itself to make people do things is not neutral.
Also keep in mind that the actual ideals of the state in a republic, democracy, equality and freedom, might differ drastically from what people might experience. So for some the state provides agency, while for others it denies agency. So it has a radically different meaning depending on which group calls for "less state" or "less regulations". Like if a monarch bound by a constitution complains about "regulations" and demands "freedom", what they're calling for is not "universal freedom" it's personal privilege to the point of tyranny.
So unless you're talking about universal principles that apply to everyone equally freedom can become a zero-sum-game where one person's freedom is another one's servitude. Similarly restricting someones excessive agency can be a necessity for someone else to have agency at all.
Essentially the ideas of the enlightenment won so thoroughly that any political party or movement that seeks popular support has at least to pay lip service to freedom and equality, but that also makes it crucial to look what they actually mean when using these terms. Are they talking about privileges for their peer group or themselves or are they talking about universal rights? Not to mention that you can do both at once as Anatole France exemplified:
The law, in its majestic equality, forbids rich and poor alike to sleep under bridges, to beg in the streets, and to steal their bread.
Theoretically it's a universal law, practically it only serves to limit the freedom of one group.
So coming back to the left and right question. You can use them and they are used for all kinds of spectra to differentiate positions on a binary issue. But due to it's historic roots you can also identify a leaning towards Enlightenment ideals like universal freedom and equality on the left and classical conservative ideas like natural orders, hierarchies and elites on the right. Like a left winger would argue that all citizens have equal rights to life, liberty and the pursuit of happiness while a right winger would either excuse or actively seek inequality based on a variety of reasons, money, nationality, sex, race, gender, sexual orientation, ability, ...
So that is afaik the overarching theme for those. Usually looking at how much in favor or against social hierarchies a person, policy or ideological position actually is. Which is difficult because that can differ between decades and countries and there's theory and application so that people can say something very leftist and do something that would be characterized as right wing.
Also for obvious reasons in the western world the Enlightenment side has usually taken the cake so arguing openly in favor of hierarchical systems is quite frowned upon. It's rare for even right wingers to openly endorse a monarchy, state a believe in a natural hierarchy, argue for strong authoritarian leadership or repression of other ways of life. So sometimes the right is just relative to the right of the other parties. While in other cases the old ideals are just framed in the language of the enlightenment. So repressing other ways of life is framed as "exercising ones religion" or it's argued with equality of outcome vs equality of chance, so as to use the term equality while actually arguing for why inequality is actually legit. Similar with concepts of a meritocracy or a prosperity gospel. Or how freedom is only an issue when a privilege is at stake but seldom when essential civil rights are demanded, then it's an overreaching state.
So yeah these distinctions kinda fit in line but you've got to be careful with political statements as everyone tries to frame themselves as cool even if they do or want to do the opposite of what they say.