While most cougars are docile, they still have the ability to hurt others. Just as humans do not all have the same personality, so, too, are animals different from each other. Even though one cougar might not feel threatened, another cougar might feel intimidated and react violently as a result. They are large animals and people should be careful.
Yes, people should be afraid of cougars. Though known to be more docile with humans than other big cats, they are still wild animals that ought to be accorded the proper respect and kept at a safe distance. If humans stay away from cougars, there will be little chance of cougar-inflicted injuries. Also, wild animals ought to be left in the wild to live as they would without unnecessary interference from humans.
Wild animals cannot be trusted. Just because they are USUALLY docile does not mean they will ALWAYS be docile. People tend to get too comfortable with mother nature and it tends to end badly for them. Like the guy that was eaten by bears who thought they were his friends.
Yes, people should be cautious of interacting with cougars because they have a tendency to react aggressively and could pose harm. Even though some cougars are docile with humans, it is often a result of intense training and trust built between the human and the cougar. There is never a guarantee that a cougar will not react violently.