There are far more pedestrians than cyclists. You need to prove likelihood so, cyclists per head injury compared to pedestrians per head injury.
The uncomfortable part and the one always avoided is simple. Helmets can only prevent a head injury if an incident occurs. Therefore i is appropraite to actually look at hospital admissions.
Look at any cohort study of hospital admissions. Sharon Thornhill's paper is a good start, or you could try the NICE guidelines on head injuries. In all of these cases cyclists do not feature as an "at risk" group.
Then we have the Maths...
100 head injuries are admitted.
In all Cohort studies the number of pedestrians is between 5 - 30 times the number of cyclists
Lets assume helmets work and take the lowest figures....
We will still prevent 5 times as many head injuries if pedestrians wore helmets.
What you now need to do is explain why we shouldn't prevent the greater number. Are pedestrian helmets less painful, less traumatic, or are pedestrian head injuries acceptable to you and therefore not worth preventing?
We could also take another paper from the BMJ...
Of at least 3.5 million regular cyclists in Britain, only about 10 a year are killed in rider only accidents. This compares with about 350 people younger than 75 killed each year falling down steps or tripping
So 35 times more people will die on stairs than cycling!
Should we be making helmets compulsory for stairs?
Or are you again going to somehow prove that these head injuries should not be prevented
not proof that a pedestrian journey is more dangerous than cycle journey
Wardlaw (BMJ) and others would dispute your stance!
Six times as many pedestrians as cyclists are killed by motor traffic, yet travel surveys show annual mileage walked is only five times that cycled; a mile of walking must be more “dangerous” than a mile of cycling.
In with keeping with anti helmet wishes for hard evidence you will have to show evidence to support your claim, or it will be discarded
Care to explain how advocating expanding helmet use to the groups that suffer the most head injuries is "anti helmet"?