It’s hard to know for sure if when it seems he’s crouching if that’s because he’s trying to pick up something to use/throw. However, crouching makes him look smaller, and this also seems to coincide with when the cougar lunges and acts more aggressively, as he’s leaving himself more open to her because crouching makes him less physically imposing. A horrifying situation to be in. Plus it’s difficult to manage much when the cougar can cover so much ground so quickly if he tries to grab something.
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Animals don’t do that. In the animal world, you need to hunt and kill every meal to survive. Getting even a slight injury could mean you can’t catch anything for a week and then are too tired to hunt even after healing. Most predators are super (cats). That’s, why making yourself seem big and loud, is basically rule #1 for every wild animal encounter. 95% of animals will turn tail and run at the first whiff of danger.