If you see a spider on the ground and you don't want to get bitten by it, you can simply wander away. If a dog wants to bite you, they can run after and injure you badly, possibly kill you. They are top predators after all. At least this dog apparently didn't have an owner to blame you for you making their dog bite you.

The key point is that the situation is not symmetrical. Some fears are far more justified than others.