Though for many people wearing a cycling helmet would not change their present riding practices, there's an expectation children / people on small profile bikes would benefit the most from wearing one, (ie safer,) however there are good reasons not to make them mandatory.

As already mentioned it can interfere with constant checking habit for extra safety, as well as cold weather appropriate headgear. Personally I gave up cycling once compulsory helmet laws were introduced in Australia since for sun protection I had an already heavy enough wide brim weather proof hat. It's probably not that common, but I have a weakened neck from a poorly treated bad whiplash (forced over the edge of road on a bicycle with a wooden road marker being right at the spot my head / neck area would land.) Additionally trying a helmet (not all helmets are the same and possibly there are brands out that have addressed certain problems) I found the straps sitting proud interfered with other distant road noises, not an issue in town traffic, but it would certainly drown out vehicles approaching from behind driving on non urban roads, with many drivers not looking for cyclists sharing that road.

I'll chip in with my main reason, as a London cycling veteran of nearly 10 years: shoulder checks.

I whip my head back and forth over my right shoulder constantly to check the state of traffic behind me.

Before I maneuvre, I check, check and check again. Always checking. Always fully aware of what's behind me.

Having something attached to my head makes it harder and less comfortable to do these rapid checks. I think this makes me less safe overall.

Several of the reasons are shown elsewhere in this thread, but here's one I haven't seen here yet:

Because I like my head not freezing when it's ten degrees below freezing? When I bring this up, sometimes people tell me about thin membrane caps that fit under the hat, but they don't work when it's actually really cold out. Helmets absolutely do not fit over warm-weather hats (or any hats, really). (Other people have said "why would you be biking if it's below freezing", which shows that they don't understand the entire conversation.)

Same reason for not wearing one in a car, bus or when crossing the road, I guess. Some people just like to take risks.

Having to carry it around. People who say you can just clip it to your bike haven’t lived in any city I’ve lived in.

What possible reason is there not to wear a helmet when driving a car?

Helmet hair. Once my hair gets compressed by a helmet, nothing other than a shower can fix it, and we don't have showers at work [not an issue as I'm remote now].

I live less than a mile from my former cubicle, and my old commute was mostly through a park with two road crossings. There was no reason to wear a helmet.

If I'm on a longer road ride, or riding off-road, I religiously wear a helmet. If I'm riding lift-assisted downhill, I wear a full-face helmet.

I wear a helmet 99.9% of the time on a bike. They are not zero hassle. If you live somewhere where stuff gets nicked in public and you’ve got a nicer helmet, you bring it inside your destination with you. They mess up hair too.

They’re not GOOD reasons but let’s not pretend there aren’t any at all.