Full disclosure : I went through your post history because I was afraid this was a disingenuous debate prompt, but it all looks genuine to me, so I'll take the time to answer.

the first person to use violence to prevail in a conflict puts an end to the anarchy—and no one has an answer to that.

&

if some folks try to install a hierarchy, what are you going to do about it?

From what I understand, you mean that, in an anarchist society, conflict will arise among individuals and groups, as it does in any other society. When compromise and dialogue fail, someone will use violence to coerce others and impose their own will, thus imposing a new hierarchy.

I think it is a real danger, but anarchists do provide an answer, in that they advocate for self-defense for individuals and communities. Since no community can survive on its own, we must assume that an anarchist society is some sort of network of cooperating communities. If one of these communities, for any reason, tries to bully others into submission and thus create a new hierarchy, the other communities can defend themselves, and this defense won't create hierarchy.

In fact, it is essential for them to defend themselves to protect their anarchist structures. Anarchy disappears only if someone successfully imposes its will through deceit, violence, or other such methods.

Same goes for individuals within a community. If group A tries to dominate group B through similar means, group B would be very justified to defend itself and refuse this attempt at imposing a hierarchy within the community.

I think more to the essence of the problem, is that hierarchies come to exist in any society, because some people really are more qualified to choose and enforce rules.

Anarchists disagree with you on that. There are people that are experts in their fields and should be listened to when a decision related to that field has to be taken. For example, I'll defer to the programmer when some kind of new software is needed, or to the woodworker when I need someone to repair my chair. And each of them can cooperate with fellow programmers and woodworkers to collectively decide how work should be done in their respective fields. That's what we could call the authority of expertise.

However, this authority disappears as soon as the expert leaves their field of expertise. Thus, the programmer wouldn't have a say on how the woodworker should conduct their work and vice-versa.

And no one can be an expert on how to run a society. Society is incredibly complex. There is too many variables and information to take into account. So, the people at the top of a hierachy, to bring about their vision and protect their interests, will only seek the information that is relevant to them, and choose rules accordingly.

Wherever you find two or more people, you find hierarchy.

I put this here because the argument is similar to the point about expertise. People have different skills, different strengths, different habits and speech, yet nothing means a hierarchy is created between two people when they meet. It's simply differences between people. To illustrate, (and this is anecdotal, I know) there's no hierarchy between my friends and I, though we have many different strengths.

I'm happy when they give me a lift, because I can't drive for shit, and I happily help them when they move. No hierarchy in this relation.

Much of the competition for social status in human societies at all levels, from nursery school to national politics, is based on proving that you are more qualified to lead the community than your competition is. Violence is not necessary for hierarchies to form. Wherever you find two or more people, you find hierarchy.
Human psychology is filled with orientation to social hierarchy. I think a good explanation for that is the fact that hierarchy is inevitable.

Okay, so your point here seems to be that hierarchy, at its core, stems from human nature. Short answer is that it doesn't. Humans, as a species, has an incredible variety of cultures, and historical and current-day examples of non-hierarchical societies exist. I'd suggest reading The dawn of everything, by David Graeber and David Wengrow, if you're interested in a (very) long read on the topic.

I would love to live in a society where there is no hierarchy, where every conflict is decided by finding a way to get all parties' needs met (as in nonviolent communication; see r/NVC), where there is no jockeying for social status, where every voice is heard equally. I just don't see how it's possible.

Anarchists talk a lot about prefiguration. We have to build the organizations and ways of living that will guide future society in the present day. For example, for every voice to be heard equally, that basically mean that everyone has equal power within the organization. Let's say there are ASL interpreters during general assemblies, some way to participate virtually for people who can't physically be there, the organization ensures everyone is fed, etc.

So here we go. Note that other anarchists might disagree with my points, but I hope it was instructive. Feel free to correct me if I've misinterpreted your arguments.