There is no such thing as Anarchy. It's a myth or an oxymoron. Put 3 kids (age 5) on a playground, and in 5 minutes they'll have defined the rules for a game and how they want to play. Anarchy is unstable, and it quickly decays back to a stable state of a libertarian or minarchist kind of government (military, police and courts), protect individual and property rights, and that's it. Then the right spreads out from there. Since there is no true anarchy, and the right starts usually to the left of minarchy (with some social programs, regulations and laws beyond just personal property/liberty), the right starts well towards the center, and moves left. While the left starts on the far left, and moves lefter.
Family units, tribes, fiefdoms, kingdoms, religions and governments all evolved from anarchy. Humans crave order and constraints, and a bit of hierarchy. Thus if you leave groups to their own devices, they make rules. As the group gets bigger, they break into factions based on what they care about, and fight for different rules (politics). But that's all about order. So anarchy is an unstable element, and it evolves to a libertarian state. And one faction always wants more government/authority than what we have, and another wants less.
Left and right are inverted terms in Europe and America -- but in America, the left is the one that wants elitists ruling the rest and more centralized power, and telling us what to do, for our own good. And the right is the group that wants less authority, more religious freedom, more free speech, less regulation, and so on. They do have issues they cross on -- the left wants less consequences for breaking the rules, and the right is about more order and consequences. The right also can cross over and want rules on morality that align with their religious beliefs -- but the left has plenty of those too (like environmentalism, social justice, redistribution of other people's wealth, and so on). But as a general rule, the more leftist places in the country are trying to micromanage people's lives, and the rightist places more want to leave people alone at the federal level, and even at the state and local levels.
Libertarians are anarchists - There is a reductio ad absurdum argument by the left, that Libertarians are all anarchists, or it would lead to anarchy. This is like saying anyone for a single social program wants complete Authoritarian Marxist Tyranny. There might be a few that far out on the bell curve, but they're not the norm of the movement, nor close. This also devolves into idiotry about "who would build the roads, schools, police". We had all of those back before we had an IRS and were far more Libertarian than most Libertarians today would want -- so it's an argument that appeals to the ignorant or partisan, not the informed. We can debate how extreme a Libertarian is, and whether they are an anarchist in Libertarian clothing (and there are a handful out there). But saying Libertarians are anarchists is like calling all Democrats rapists, just because Bill Clinton was one.