Well...this IS A&S where anything can be disputed.

A helmet only increases your safety IF you hit your head just right. And the helmet makes your head substantially LARGER, so you are more likely to make contact with an object than with your bare head. How many head injuries could have been avoided if the head had not made contact with the ground without the helmet?

There are many people who will not ride a bicycle if they are forced to wear headgear. <-- This will certainly makes them safer from a cycling head injury, and can not be disputed!