I agree with @
Lester Polfus. I think it was maternal defense--at least in the first 30 seconds. After that, I think she was trying to decide if she could take him without risking injury. One thing I learned from a wildlife guy is that most predators are usually very hungry--like what it would be like for us to have not eaten for a day or two. I think she thought the dude looked like a tasty meal for her and her cub(s). My guess is this was 6 minutes of testing her prey for weakness. If he had turned and ran after one of her charges, she would have attacked. As soon as he showed he had fight, she was done with the hunt and went back to her cub(s).
From what I know about cougars, showing that you are a threat is essential. It's hard to know what the right answer is, but if I had been in that situation I would: 1) put my fucking phone away, 2) stand tall, with arms in the air, and yell, 3) back away slowly from the cub area for a short distance 4) get rocks and go on the offensive, 5) keep two big rocks in my hands after the cat ran and stay frosty, because
they can return and kill you.
Oh, yeah... and not go in the backcountry alone and unarmed.
Maybe. In the post I described at the beginning of this thread, my wife and I did see them coming, and I was able to draw my gun, get a good sight picture, and prep the trigger. Cougars are stealthy predators, but humans have excellent vision when paying attention, and are taller than a lot of other animals. They were hiding very effectively in tall color-matching grass, but we still saw them.