Oh dear, the price of fear.

Someone in another thread aptly distinguished between dangers and fears. It helps a lot if you can calibrate your fear to reflect the actual amount of danger you face. All too often fear is the product of unbridled imagination, only loosely connected any real danger.

As others have pointed out, the odds of being attacked by any creature (including the two-legged variety) while backpacking are vanishingly small, whereas the odds of getting hypothermia, or even being struck by lightning are substantially greater, and just as deadly.

It's just that imagining dying of hypothermia doesn't inspire the same flesh-creeping horror as imaging being torn to bits by a rampaging bear, so we focus on the more horrific idea that is almost certain not to happen and we discount the much greater danger that kills hikers by the dozen every year.

This is a design flaw in our brains.

Generally speaking, any strong emotion we experience is designed to fix the memory of the event that caused the emotion indelibly, so we can never forget it. This has many benefits for learning when the event is a personal experience. It can even allow us to learn from the experiences of others, by imaginatively placing ourselves in their position.

But this mechanism goes haywire on us pretty often, too. The fear of wild animal attacks is typical of this.

So, carry the gun if it makes you feel better, but you're much better off putting your energy toward dangers that you'll encounter in real life, rather than in imagination.