Historically, anarchism arose out of left wing movements, that ground has been covered in other answers so I'll leave that at that. However if you're intent on forcing all political ideologies and philosophies into this narrow framework of understanding, and somehow want to find some utility in it, I think it's also worth examining and understanding the history of this framework.
The idea of there being a spectrum from left wing to right wing originates from the French Revolution, where those who supported the establishment sat on the right, and those who sought to overturn it sat on the left of the assembly room. Throughout history, movements, ideologies and philosophies have been categorised as left or right according to a large array of criteria - the definitions from Wikipedia are a pretty good summation of this array. Now if we look closely at that array of criteria for assigning the labels 'left' and 'right', the common threads that appear are that leftist traits tend to be opposed to the establishment, concerned with change and 'progress', where as the traits associated with the right wing tend to support the establishment, and are concerned with opposing change and maintaining existing (or reverting to historical) arrangements of social relationships. Even Fascism (which is another ideology which defies the right-left dichotomy) can be placed on this one dimensional axis using these boiled down criteria.
According to this analysis anarchism is broadly speaking a left wing grouping of philosophies, as opposition to hierarchal authority (which is the common thread uniting all anarchists) can't be reconciled with supporting the establishment or conserving existing social arrangements. Anarchism is inherently opposed to the reality we live in.
The question is why would you want to use a reductive framework to try to all-encompassingly organise the history and current reality of political thought when to do so you have to reduce the framework even further? The only use I can see is if you're trying to make sense of politics objectively, assigning essential meanings to the names of ideologies like 'anarchism' and 'communism' which are supposed to mean the same thing to everyone. The problem is that politics is subjective and can't be made sense of objectively, trying to do so is a particularly bad habit of westerners, and more specifically Anglophones. Maybe it's because we're raised in liberal democracies, and the political language of liberal democracy - the words, phrases and concepts that liberal democracy uses to define itself, and as it happens our native political language - doesn't allow for subjectivity. Liberalism after all is a child of The Enlightenment, a period of time when we became obsessed with science, assigning essential meanings to things, and naming them to add to our ever expanding lexicon of nouns; and so it makes sense that the political language (and intellectual technology) that our upbringing equips us with is with is unable to deal with the fact that ideas and their names mean different things to different people at different times, and so words and concepts like 'anarchism', which are highly disputed and whose locus of ideas (the desire to be not be ruled) doesn't have anything to do with the loci of the objective right-left axis (progress/change vs conservation/stasis), are something that we have trouble assigning essential meanings to.
My solution has been to shed the political language that liberal democracy uses to define itself, to stop using it to try to understand ideas that are opposed to it, to stop trying to assign essential meanings to things and instead look at what things mean to me, what they mean to other people, and acknowledging any differences between the two, instead of trying assert an objective judgement of them. Of course I'll still assert subjective opinions, like 'anarcho-capitalism isn't consistent with anarchism', but that doesn't mean I have to assert an objective judgement - I can say 'anarchism means x to me, to me that is what anarchism is, even though you disagree' without asserting that someone else's anarchism is objectively wrong. Instead of trying to understand an ideology or philosophy from an external locus, I try to understand them by seeking out their own locus. I don't try to understand anarcho-capitalism by looking at it with anarchist concepts and frameworks in mind, I go to it's origin and focal point - classical liberalism. It's also why I use the term 'anarcho-capitalist' instead of some derogatory term, because it's the endonym anarcho-capitalists use to describe themselves. Anarchists have over hundreds of years developed their own frameworks of concepts and language to describe and discuss anarchism; they are the most relevant and useful frameworks to anarchism because they originated within it.
Sorry if that's confusing or hard to follow, I find it hard to talk about mental tools incisively and clearly XD