Why should a person never stare at a strange dog?

This depends on the type of dog. Most smaller, friendlier breeds probably won't do anything except lay there or try to play with you. However, getting in a bigger dog's face and staring it in the eyes is a very bad idea. Keep in mind that a lot of the bigger dogs have been bred to behave and perform certain ways. When you are looking a more aggressive breed in the eyes, you essentially provoking it. Dog's have body language like us, and in "dog body language" looking at someone directly in the eyes is a challenge.

If you are the dog's owner, have raised it for years, and have a positive relationship with the dog the chances of being attacked after getting in its face aren't so likely. But it's better to be safe than sorry.