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"Is a bear more like a dog or a cat?" - That's a sure way to die. There's a tiny chance of slashing its belly and, while it's trying to stuff its guts back in, attempting to escape, but it's a tiny chance.
"If you encounter a wild cougar/wolf/leopard, 99.9% of the time, you won't even have time to be scared, let alone draw your knife." - That's just your imagination. Watch animal fights. See how cougars and leopards first attack large dogs, and then, after unsuccessful attempts to kill them, they run away. I haven't personally dealt with leopards or cougars, but I know cats very well. And I have experience with dogs. If I know that I can deal with a large dog even without a knife in 90% of cases, then with a knife, a cougar, leopard, or jaguar has no chance against me. But against a tiger or a lion, I have no chance. Therefore, I would eliminate them.
"I heard that animals are terribly afraid of the human voice." - Not at all. They're not afraid in the slightest. It's just that dogs have hearing 50 times better than humans. That's why so many dogs get lost during New Year's holidays. Imagine 50 firecrackers exploding at once next to you... And a voice... Well, would you like it if 50 people shouted at you at the same time? The voice isn't the main thing. The main thing is to remember your advantages (higher primates have strong bones. Striking techniques against vulnerable spots of animals work great) and the weaknesses of cats and dogs (it's easier to break a cougar's ribs than a human's).
Added 3 minutes ago
"Tigers are an endangered species and don't try to attack humans." - Read Wikipedia. The Champawat tigress killed 436 people in Nepal and the Indian region of Kumaon.
Added 32 seconds ago
"Tigers are an endangered species and don't try to attack humans." - Read Wikipedia. The Champawat tigress killed 436 people in Nepal and the Indian region of Kumaon.