I think the question (+subtext) is somewhat misleading for several reasons among those a) just because something seems "natural" it doesn't mean it is logical, necessary or legitimate. Animals kill other animals for food, its "natural" but it doesn't necessarily translate to human societies; b) there are many types of hierarchies across our "species" and some may be "necessary" for some specific purposes, while others are not.
Hierarchies in human societies usually fulfill or fulfilled a specific purpose within a specific rationale, or world-perspective. They are one possible element (although common) in the (vertical) organization of specific groups and they imply, by definition, a social relation between unequal parts. I don't think there's much point in questioning the principle of hierarchy in relation to the whole species, but only to specific groups or societies.
So it is perhaps more relevant to question, for instance, what is (or was) the specific function of a given hierarchy within the social relations present in a specific social organization (group, city, state, country...). Why does a specific hierarchy exist? Who profits, and who is to lose from the implicit relationship? Is that hierarchy promoted through any form of explicit or implicit ideology? Is the hierarchy itself even acknowledged by every participating party? How do they perceive that relation? ... and so on.
The way I see it, anarchism, in the broadest way possible, is just a different way of organizing society. You could say that it is, in principle, averse to hierarchies since it is usually based around mutualism and collaboration among equals. That means equal rights, equal opportunities and equal responsibility. Anarchy assumes that it is possible to organize society without vertical relations where one party has power over the other. That doesn’t mean there would not be some kind of normative power (laws, for instance), but that the normative power within a society should function to assure those principles of equality. Because only through equal possibility for participation can that power be legitimate.