The article makes a good point, and there are arguments on both sides. However, to say that Amsterdam and Copenhagen are places that have a significant portion of the population using bicycles on a regular basis, and they don't mandate helmets and yet everyone's safe is oversimplifying the point in a way that's detrimental to the discussion. Even if we grant that this is the case, which I have no reason to doubt, it's not like everyone woke up one day, ditched the helmets, grabbed bikes and rode around. If a majority of folks in a given place ride bikes, it's safe to say that's a culture that understands and respects bicycling as a mode of transportation, and has experience combining bicycle and motor vehicle traffic in a safe way. Cyclists are comfortable with cars and vice versa. One of the things that helps contribute to accidents is nervous drivers, nervous cyclists, or a combination of the two. I'd also be willing to bet there are more bike lanes in places like those mentioned in the article.
Helmets may make cycling seem more dangerous, but living in a car dominated culture where many places do not prioritize bike safety actually does make cycling more dangerous. No, a bike helmet won't protect me much if I'm hit by a car. In that case, I'll be lucky to escape with just broken bones. However, a helmet certainly would protect me if I'm riding between traffic and a row of parked cars (like cyclists in many cities are forced to do if their bike is their main source of transport) and I have to swerve to avoid a car who doesn't see me. In that case, I'd rather be wearing a helmet when I hit the parked car or the pavement. And, I'd rather be conscious and able to get my bike and myself up out of the street rather than being knocked out in the middle of the street and causing a bigger problem because folks have to go around me or come out in the road to help. Helmet laws aren't there to force people who could care less about their skulls to put clunky helmets on. It's to protect the other folks who would be dragged into or affected by an accident that would be exacerbated by someone not wearing one.
Bottom line, wear a helmet. Do it for the children.