Why do dogs lick people's skin?

It's an interesting question, so let's start with why they lick their own wounds first. First of all, a dog's saliva is very clean, as compared to a humans. And of course, their saliva contains enzymes, etc. which aid a dog in both cleaning their wounds and to promote healing. The second reason is most likely, instinct. After all, they lick their wounds, so why not yours, and for the same reason, just as a mother dog would lick the wounds of one of her pups, should it get injured. It's strange, but after a period of time, you realize that the dog isn't as much your pet, as you're theirs. That's where the training begins, and you've got a lot to learn. Don't worry though, it won't be long before you're properly trained. Seriously though, I wouldn't encourage a dog to lick your wounds, but I wouldn't yell at it for doing so. Just a simple pushing away at the muzzle and a gentle, "No" should be enough. Chalk it up to praternal/maternal instinct. Our canine friends are a devoted species, and they too feel that they must take care of their human pets.