I'm not sure that there is a simple A, B, or C answer to this. Although if forced, I would say C: Both.
I think part of the problem is what we mean by hierarchy when we say that. If you are talking about parents (or, in societies without nuclear families, adults- parents, aunties, grandparents, etc) in relation to children, some hierarchies will likely always exist, although it is important to note that in many societies where the power of adult influence is more diffused, there is less rigidly hierarchical relations between generations. Words like hierarchy, power, and authority get thrown around in a pretty reckless way in anarchist circles (I am certainly guilty of this), and that tends to leave all of them meaning maybe the same thing? But certainly nothing concrete.
In regards to the relationship of an employee to a boss, that is a clearly hierarchical relationship in a concrete way. Your boss maybe wouldn't sack you, but as your boss, he could sack you, which cuts you off from your means of survival in a relationship that is purely about capitalism (even if it is a charity - I work for a not-for-profit myself, but we are still complicit in and help maintain the larger system of capitalist relations).
Unless your parents are wielding your financial dependence on them over you in a similar way, this is different (and the way you refer to them in your question, I am assuming your relationship with them is mostly okay, so if not, my answer might change).
(Aside: There is a dumb old Bakunin quote about boots or shoes or something that you can look up if you really want, but I never particularly liked it.)
Regarding individual choice: sure, it is up to the individual, but I would be careful about this argument - it is really easy to fall into anarcho-capitalist terrain if you uncritically use arguments like this. As an example: I have a friend who is a pro-dom. People pay this friend to dominate them, but they are choosing to do so. Entirely voluntary relationship. That is different than me going to work and having to do what my boss tells me because I need to or I don't get paid anymore and then I can't pay rent and am homeless.
This gets back to capitalism, but I think there are other forms of capital that need to be considered, such as our social capital. It might not be a monetary relationship, but there can still be hierarchies that are undesirable or constraining.
I'd try to write more about that, but I am tired and need to sleep now...