I can't understand why people refuse to wear helmets when riding.

Because wearing a helmet makes you more likely to be in an accident and increases the risk of brain injury when you are.

The first has two causes:

• People take more risks when they wear helmets. source1, source2 source3
• Cars are less careful around riders wearing helmets. source

The second:

• A helmet effectively makes your head larger, and as such increases the risk of your head hitting the road. In fact your risk doubles. source
• A helmet protects against ‘focal’ injuries, that is injuries at the point where your head hits something. But a another type of brain injury is ‘diffuse’ injury, basically the fact your head hit something at all, and your brain rattles around in the skull. This type may cause worse problems than focal injuries. The added size of the helmet amplifies the rotation of your head on impact and makes this type of injury worse. source. Add to this the fact that wearing a helmet makes you more likely to hit your head in the first place.

In addition to this, wearing a bicycle helmet makes cycling less attractive, and as a result people will cycle less. This results in a loss of health benefits from cycling.

Sure, intuitively you might think a helmet will make you safer, but intuition is often wrong. When you look at the actual data it shows a different picture.