This is a really similar answer to several other answers that are on this site. At some point I might feel motivated enough to search by tags and find them, if so, I'll link to them, but probably I won't.
First off, to nit pick: If the people you are talking to use terms like "a condition of anarchy" I would speculate that they are thinking of a very different situation than what most of us here are talking about. "Condition of anarchy" conjures up images of Somalia in the mid to late 90's or Afghanistan under the rule of various warlords. In both of these examples, there are numerous groups existing without a central state, but within the prescribed borders of a supposed state. Here is a question that might address some of that: http://www.anarchy101.org/2722/is-somalia-an-example-of-an-anarchy-and-if-not-why
Moving past that, I think we should keep in mind that millions (well, to be honest, billions) starve and die or have already done so under capitalism. Take, as an example, the famine in Ethiopia in the mid-90's, which was triggered by governmental policies (drought only exacerbated the situation). The Great Famine in Ireland (1845 - 52) was similarly a man-made phenomenon: although the potato crop failed, Ireland was exporting enough grains to feed the population. What people who object in this manner often mean is that they might starve and die, because they don't actually produce their own food, so without global trade and commerce, they might not get the food they need, or at least the food they would prefer to eat.
Millions (or billions) might starve in an anarchist future. Probably they would, but that doesn't invalidate anarchism any more than it invalidates capitalism.