I tend to share this attitude. As an avid cyclist I have been chased by dogs many times. They can sense fear, but they also know when you don't show any. I'll jump off the bike if an attack seems imminent (and it is a dog I can't out sprint) and bow up at him, yelling and posturing aggressively, and so far that has always shut them down. Except one big old hound out in the country in Arkansas. He didn't seem impressed so I had to give him a whiff of pepper spray. That did it.
Cats, not so easy to scare away. Think of an 80 lb. bobkitty, probably not going to attack you. Now, a 180 lb. mountain lion, you better be armed and ready. Those things are solid muscle and fighting spirit.
I was out hunting for hog and think I saw a panther a short way off through the trees. It was just a shadow about 50-75 yds off through the thick brush and trees.
I was praying he wasn’t stalking me. There is no way I would see him coming if he chose me for dinner.