There is none. If helmets made a significant contribution to safety, than as more people wore them, fewer would get injured. But that hasn't happened. As helmet use has increased, the incidence of serious head injuries to cyclists has not declined.

In some ways this is not surprising. In the first place, cycling - ordinary cycling, just riding along, commuting etc. - is very safe. In the UK there is only one fatality per two million miles cycled. In the second place, the most usual cause for serious head injury among cyclists is collision with a motor vehicle - and even the manufacturers don't pretend that helmets will offer much protection in that scenario. Indeed, the incidence of head injury per mile travelled for cyclists is approximately the same as for pedestrians, and for the same reason - collision with a motor vehicle. So those who say there is a need to wear a helmet for cycling need to explain why they don't wear one while walking across the street. After all, there's no reason NOT to wear one, is there?

Promoting the idea that cycling is so dangerous an activity as to require protective clothing just discourages people from cycling. It isn't.