First you need to know that bike riding can be a very safe activity.
Many, many people have ridden for years and years without ever coming close to actually needing a helmet. So the overall improvement in safety for the whole population might not be so big after all, even if all were to use helmets.
The theory is then that quite a few people think that bicycle helmets look stupid, and/or messes with their hair more than they're ready to put up with.
There's also a concern that the recommendation to use helmets makes bike riding sound so dangerous that people don't want to ride any more.
So if society were to enforce mandatory helmet laws these people would stop riding.
And with less bikes on the streets, cars will be less likely to look out for them, increasing the overall injury rates.
Me, I don't really care about the statistical details. For what helmets cost, how easy they are to wear and the protection they offer, I'll happily use them.
A helmet may or may not save my life, but even if it only saves me from splitting an eyebrow I'd still think I came out ahead in that deal.