I have read about cougar attacks and it would appear that a weapon can definately increase your chances of survival. My daughter's friend, Anne Hjelle, was attacked by a mountain lion while mountain biking. She is alive because she and her companion fought back. The friend fought off the lion with a stick. Mountain lions are like all cats and are frightened by loud noises. A gun of any kind would have been way better than a stick. For a summary try reading
As for bears, while they are usually after your food and can be driven off, sometimes they decide to eat you. In that case , you had better be ready to fight anyway you can. Playing dead when a black bear is trying to eat you is going to result in you being eaten. In nature(not the movies) animals do not kill everything before they eat it. When the critter is trying to eat me. I want to be able to fight back in the most effective way. I don't pin all of my hopes on a firearm. I also carry pepperspray and am almost never without my knife(which is either a fixed blade or one hand opening). I plan on keeping my spot at the top of the food chain. Below is a recomendation of what to do if threatened by a cougar. It can be added that you should never run from a cougar or a bear. With bears. you should speak calmly and back slowly away but if it comes for you, get ready to fight.

If a cougar behaves aggressively:

Arm yourself with a large stick, throw rocks, speak loudly and firmly. Convince the cougar that you are a threat not prey.

If a cougar attacks, fight back! Many people have survived cougar attacks by fighting back with anything, including rocks, sticks, bare fists, and fishing poles.

Finally, gun ownership and use is a personal choice that brings with it a huge responsibility. I would not give my seven year old grandson a chainsaw but I did give him a .22 rifle and have taught him gun safety and how to shoot. The bottom line is a gun is machine without a mind of it's own. Much like a car and to use the logic that guns can be used carelessly and cause injury, then I guess we shouldn't have cars either. Our safety is like every other aspect of the sport of backpacking. We all make personal decisions on what we need or want to take.