That reminds me of a time a loooong time ago (pre 1971) when I was out dove hunting with my trusty single shot Stevens 12g in SW Oklahoma.
I was in a sparsely wooded area when I stepped around a tree and about 12' away was a big cat using another tree as a scratching post.
I can remember to this day his color and how he was stretched out with his big paws further up the tree than I was tall. While in that position he just turned his head and took a good look right at me. I knew right then I was screwed, I had a single shot 12g loaded with 7 1/2 shot and a few shells in my pockets. If he decided I was lunch we were going to the rodeo. I figured the best thing to do was to leave, if I could. Holding the gun at a loose ready I started to back away slowly, all the time keeping my eyes on the cat. About this time he took another scratch at the tree, went back to all fours, turned and went away from me.
On the way home I stopped by the local Co-Op because I saw the local Fish and Game officer's truck there. I went in and told him, and a few of the ranchers there what I saw and was immediately rebuffed by the fish cop. He said there have never been any big cats in that part of Oklahoma. I begged to differ with him, as did a couple of the ranchers, but he wouldn't be convinced. Or he knew and was spreading disinformation, which seems to still be going on.
That was probably one of the most scary times I ever had when out hunting. I was out alone, in a fairly remote area and if that cat had decided I looked tasty it could have gotten ugly pretty fast.
Cats are quiet, superb stalkers and you often don't even know they are there. When I go out hunting coyotes in cougar country, I try to take a partner. I will for sure when I do dedicated cat hunting.
bob