Yes, you read that right... riding your bike without a helmet may be safer than riding with one.
Statistics are an interesting thing. They can very quickly relate large amounts of information. The problem is that without careful analysis they can create the wrong impression or give an altogether false understanding of the world.
Why It Makes Sense to Bike Without a Helmet is a simple example of this very concept:
People have tried to reason with me that because I’ve spent so much money and time developing my brain, and the cost of an injury would be so devastating, it’s clearly more important to wear a helmet. But if we start looking into the research, there’s a strong argument to be made that wearing a bike helmet may actually increase your risk of injury, and increase the risk of injury of all the cyclists around you.
The main points he makes are all valid, the sources are legitimate. What he's essentially saying is that if you get into certain kinds of accidents then having a helmet on is likely to decrease the severity of your injuries, but (and this is a big but) the fact that you are wearing a helmet possibly increases the likelihood that you will get into an accident in the first place.
That second point is important, but it is often overlooked. After all, our goal should be to reduce measurable injuries, right?
Well, no, it shouldn't be. The goal should be to teach awareness and responsibility. That's hard to do.
But we can at least try to reduce the overall number of accidents resulting in any kind of hospitalization. With this in mind, the fact that wearing a helmet increases the likelihood of an accident in the first place is an important piece of information. We don't know for sure that wearing helmets is a risk factor for accidents, but there are correlations that indicate something might be going on.
This sort of secondary effect is hard to measure, but it is important to understand. Simplistic rules or laws fail to recognize that the world is a made up of complex interactions between multiple systems. Just because a simple statistic sounds good doesn't mean it's actually good for society.