How do herding dogs drive away wolves and protect flocks of sheep when we know wolves are stronger than dogs?
I see two reasons: the first is that domestic dogs have been selected to be overly confident and self-sacrificing whereas wild predators are more careful, and the second is that the stakes are different: protecting the pack is more valuable to the dog than killing a pack member/sheep/et cetera is to the wild predator, and so it will take less force on the dog’s part to “win” as the predator will just move on and try something else.
Wild animals need to be very careful with whom they choose to fight with and will generally engage as a last resort only. The same is true for what they choose to hunt: a pack of wolves can take down a full grown elk, but if one wolf breaks a leg in the process, was it worth it? A small injury is often life threatening in the wild and it’s just not worth taking the chance. There is no ego involved. The “game” that wild predators are playing is “get food in the most efficient and safest manner possible”. If killing a sheep from a domestic flock involves receiving a few punctures from a farm dog that later become infected, it may not be worth it, unless the predator is desperate.
Domestic dogs, however, play a different game. Humans have selected dogs that self-sacrifice, and will not back down from a fight even if it means certain injury. It’s not uncommon at all for a smallish dog to drive off a bear. When two wild predators get into it in the wild, it’s often not an actual fight, but “threats” and displays of confidence. The “victor” can be the one who displays less fear and never has to actually engage. Humans do this too, of course. If these are the rules that a wild predator plays by, it’s not hard to imagine why they would back down from an overzealous domestic dog who is playing by different rules.
This might be true across many areas of life, but it seems natural to fight harder to protect what one has than to get something that one doesn’t have. A wild wolf sees it the same way and may make the decision to move on from trying to kill a sheep that is being protected by a dog, but if the dog were to wander into the wolves’ territory and try to kill a pup, the dog wouldn’t stand a chance. It’s a question of value: the dog values protecting the sheep more than the wolf values killing a sheep.
One more thing to note is that the wild animals (especially predators) that remain in nature are very wary of humans, and for good reason. These predators see dogs as an extension of humans and, as such, treat them differently than they would otherwise. Also (and this isn’t always the case), since wild predators tend to be wary of humans, they take a “get in and get out” approach to encroaching on human territory for a meal. They have one foot out the door anyway and a couple dogs showing up is enough to get both feet out the door.