Anyway, it's not at all idiotic to think that there might be a sound statistical (or at least numerical) basis for rejecting an item of protective equipment on the basis of increased risk or higher costs compared with not wearing one.
We could, at an individual level, undertake a basic cost-benefit analysis of helmet wearing or not wearing and show, depending on what values we attach to some of the variables, that there is more risk associated with wearing a helmet than not. You could go further and attach notional value to injury and non-injury costs (such as discomfort, perspiration, feeling cowed into submission by an irritating social norm etc) and conclude, again non-idiotically, that the costs of helmet-wearing outweigh the benefits, especially when the costs, even if they are minor, accrue all the time the helmet is being worn (and maybe even when it's not being worn) but the benefits are only realised if you experience an incident within the operational limits of a helmet.
I think this last point is important because the benefits of helmets are routinely overstated. At low speeds, where the shell doesn't break and the foam doesn't compress, you might as well not have been wearing it and there's a plausible argument that the larger melon creates impact that might have been less with a bare head. In high speed collisions, well outside the operating limits of the helmet, it also confers no benefit so we're talking about a pretty narrow range within which incidents can 'usefully' occur to get the benefits of the helmet. Yet the costs are still borne all the time.
It's on the basis of that kind of non-scientific assessment of costs and benefits that I decide not to wear a helmet and presumably also on that basis that I'd fall into your friend's idiot category. I generally regard the risks of cycling-related injury as so close to zero as to be not worthy of mitigation, especially when avoidance is so much easier. I rely, in effect, on probability rather than safety equipment. If I rated the risk of cycling-related injury much above zero I'd probably stop doing it.
So, elaborate: explain to me why I'm an idiot.