I don't bike much any longer, but when I learned as a kid, it was just a given that I had to wear a helmet if I wanted to ride my bike anywhere other than the garden lawn. My parents didn't even suggest that I could ride without one, and the thought never crossed my mind. Bike = helmet.
The same mentality applied to horse riding. In the UK, every riding school will require students to wear a helmet that adheres to EU standards, so the notion of getting on a horse without a helmet just didn't register with me. Then I went to the US where people with no horse experience seem to happily jump on a horse and go up the trails without a helmet, which terrifies me. I am often the only person at our local equestrian events in the US who is wearing a helmet.
It's not that I feel that I'm bulletproof when I wear a helmet, and am thus more reckless because I think I can get away with it, it's just my insurance policy. I do feel safer with a helmet on, but that doesn't automatically make me a dangerous rider. I like to think it just makes me a smart rider. When I wear a helmet on a bike, it doesn't make me feel invincible, it's just comforting to know that if something were to happen, my skull has a sporting chance of staying intact. It actually feels strange not to wear one.