Anarchism merely means without a state.
Incorrect. I'm sure we're all aware that the actual definition of the word when derived from the Greek means "no ruler." Classical anarchism identified the philosophy with opposition to numerous forms of rulership, including political rule (statism), economic rule (capitalism, classical definition), and social rule (patriarchy, racism, etc). You're thinking of just the anti-statism concept, which is incomplete.
It's the left-anarchists who are trying to redefine the term to mean anti-hierarchy. They're just trying to nitpick with us, instead of bothering with substantive debate.
Actually, those on the right have done more to redefine anarchism and capitalism and the like. But the point of this isn't to point fingers, but to clarify so that we can more easily cooperate. If some people have said anarchism is simply anti-hierarchy, then they would be mistaken as well. Anarchism covers several concepts, with anti-statism and anti-hierarchy as important aspects.