I have spent a lot of time in the woods and have never had a fear of either cougars or bears anywhere in the lower 48. Alaska is a different story and I always carried a shotgun alternating slugs and 00 buckshot up there.
But, there are a lot more bears and cougars in my home state than there used tobe. A healthy animal fitting into its place in the environment is generally predictable and, common sense and a bit of training will defuse most situations. The animal I am worried about is the aging, injured, or sick one that is unable to function in its normal spot in the food chain. Then, you face the chance that good common sense and a bit of training will not fill the bill, and we are slow and easy prey...unless we have a means to protect ourselves, whether pepper spray or weapon. That is why I usually carry a Glock 9mm. It is not a rifle or a shotgun, but it is convenient to carry, has a bunch of rounds, and serves as defense for a number of contingencies. I wish I didn't have to carry anything, like I used to, but I worry about the starving, aging, animal who is desperate for something to eat.