What possible reason is there to not wear a helmet when riding a bike?

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

I do not like taking risks and I think i am a risk avoiding person.

Here in the Netherlands, I guess that my risk for getting involved in an accident, is not any higher than walking and other forms of transportation. I am not using an e-bike and I usually bike at a speed of about 15km/h. I do not use a racing bike, but a bike where you sit in an upright position allowing you to look around easily. I also take care of using routes that are safe. Here in the Netherlands, where are more bikes than cars, and biking is an important means of transportation for daily commutes and doing shoppings. We have good infrastructures for bikes.

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.

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

Seatbelts, airbags, crumple zones.

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.)

I've got a thin balaclava I've worn under a bike helmet down to 0°F that's kept me warm enough. Let out the band on the helmet a few clicks and it fits perfectly.

I think I might be quite warm naturally but those thinner caps that fit below the helmet work just fine for me when I bike in cold Sweden in the winter. -10 °C and below.

The helmet itself gives some wind protection which helps as well I think.

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.

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.

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.

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.

What's your grudge with helmets? Worst hill to die on I've ever seen.

That's not quite fair. They could be dying in ditches, on hoods of cars, against walls or trees, not just on hills.

I've seen a cyclist lying motionless on the street. Eyes open, blood coming from her nose. No helmet.

I've also seen helmets from friends who have crashed where the helmet is completely destroyed. It just isn't worth it.

Your argument is the same as that against seatbelts. I've driven hundreds of thousands of miles but never had an accident. I still put my seatbelt on.

If you really hate helmets, you could use one of these instead: https://hovding.com/

Not very practical for daily commutes. If I would not feel safe biking, I would rather wear a helmet than a device like this.

Here in the Netherlands, biking (without support) at speeds around 15km/h if you are in good health and of sound mind, is not more dangerous than walking or traveling by some other means. Recently, the number of traffic causalities has gone up, that those are mostly related to the use of e-bikes by elderly people and younger people. I feel that if you need support for biking when you do not have the strength (due to old age), you probably are not fit for biking at all. Many young people using e-bikes remove the speed restriction allowing them to bike at speed up to 30 km/h. At those speeds, the chance of accidents go up very quickly.

True, a helmet is better in all kinds of ways. It doesn't need a battery, it still works even when things hit you rather than you hitting things, and it's an order of magnitude cheaper to replace after a knock.

But if someone will wear one of these things who wouldn't otherwise wear anything at all...

Cycle routes in the Netherlands are awesome! Things are slowly improving here, but we're still a long way from that level of care placed into the design.