Yeah, you didn't explain how it wouldn't devolve into a plutocracy. Instead you supported their argument. You should have pointed out that we already have a plutocracy. How many Clinton's and Bush's do we have to have before people will realize this. Instead you might as well have told them that Hitler could rise up in a anarcho-capatalist society and so long as he's rich he can kill all the damn Jews he wants (technically true when you think about the information you've given them).
The only caveat that you mention is that rich people will be bound by the non-aggression principle, but by what? A religious man would say God, An honest man would say ostracism, an objectivist would say self-interest, but you failed to take into account what an Atheist would say. Atheists generally understand natural law so this is your common ground that you need to focus on until they might find the same logic that Ayn Rand found in her philosophy of objectivism.
It needs to be pointed out that a society in equilibrium where no force is used can remain so only if violence or fraud is not tolerated by any member. So in fact there is another premise that you must mention in your argument, that so long as no one tolerates the initiation of force by themselves or others, everyone wins.
"Anarchy in the sense of no government just ain't gonna happen -- not unless everyone becomes a hermit. A group of people will always want a system of making decisions. Even if they don't elect/designate a leader/decider. "
This poster obviously knows that people like to have rules. I would certainly not disagree. Ethically speaking, it is better to have rules that everyone agrees on. Anarchy would thus have groups that create their own rules, the members of which could be bound by contract. Be sure to mention this as well as the concept of voluntarism.
Finally the largest critique of anarchism is that it is unstable. However, I could just as easily say that any system is unstable. After all how many democracies, monarchies, and communes have fallen into anarchy over the course of human history? Thus I would propose that what we mean by stability we really mean personal security. Literally the absence of violence and fraud. However, I've already mentioned what will make an anarchist society stable, that is an absolute aversion to force, fraud, or coercion. I would posit that any society whatever you might call it would be very stable if this stability were achieved.