A question many have wrestled with. In the end, it's probably not worth the weight, as risks usually outweigh any theoretical benefit. I know some police officers who wear lycra and pistols while riding, but like a lot of good police officers, they've made enough enemies that they believe they need to carry as much deterrence as possible.
Non-lethal force for animals is discouraged. (See posts on how to handle dogs.) If pepper spray can stop a run at you by a grizzly bear better than a hand gun - well - 'nuf said.
As regards your reference to complex, 2-legged animals, I approach the question in terms of use of a firearm as extension of other martial arts. It is always a last resort. You might find the presence of your gun hampers de-escalation of a situation through your other skills.
I'll note, I did have a hunting rifle pointed at me by a drunk while sitting out a rainstorm at night in Oklahoma during a cross-country trip in 1979. A little talking to eliminate his view of me as a threat went a long way to de-escalate the situation. If I had tried to utilize a weapon, I would have been shot.
Any time you use the word gun, you'll generate a lot of discussion. My premises follow:
1. Guns are not always effective. Training, training, and more training can make them more effective, but limitations of "stopping" power of handguns are obvious.
2. One would need to wear his or her weapon - heavy and sweaty. I've used a TDI fanny pack in the past for a G19, but it leaves a big wet spot.
3. Guns can be taken away. Weapons retention training will teach you how to take someone else's weapon and why your weapon might not be secure.
4. Chances of a situation progressing to use of deadly force increases if you are obviously armed.
5. If someone in a vehicle wants to do you bodily harm, a weapon will not help.
6. If you shoot someone, you will be arrested and even if not guilty of a crime, you will likely be sued in a jurisdiction a long way from home.
In the end, I added up all the miles cyclists have travelled unarmed and without incident in the context of almost non-existent stories of intentional bodily harm outside of injuries caused by motor vehicles, and realized that risk of deadly harm in an altercation while touring on a bicycle is miniscule.
I guess, touring cyclists do not appear threatening, haughty, rich, or even good to eat....