Depends on the way you approach the question. The most convincing arguments to me are the population level ones, rather than those related to specific individual safety.
As I understand them;
1) The idea that helmets are "necessary" or compulsion by the state can lead to fewer people cycling.
There are studies suggesting that an increased number of cyclists brings an overall benefit in terms of casualty reduction among cyclists as a group that outstrips the effect of compelling all cyclists to wear helmets.
2) There is some evidence suggesting that drivers are less cautious around cyclists wearing helmets, leading to more casualties (typically in incidents that the helmets are incapable of protecting the wearer from).
3) Statistically cycling is a relatively safe activity. If helmet wearing becomes a barrier to someone taking up cycling, and they do not compensate with some other exercise/activity, it can be argued that they are more likely to reduce their lifespan than they would be had they cycled "unprotected".
Personally, I wear a helmet whilst cycling - I would not support compelling others to do so (or not).
You can get a better overview of the arguments here;
http://www.cyclehelmets.org/ including links to the applicable studies.
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