When a dog jumps on a human of its own free will, it is not "greeting" the human, it is asserting its dominance over the human; it is the dog communicating that it is alpha and/or wishes to own/control the human. A subordinate would never dream of running over and jumping on the alpha dog of the pack. Space is respect and lower members of the pack respect the higher members. If your dog jumps on humans, it does not respect them. Note: when a young puppy jumps on humans it is sometimes its attempt to reach one's face. Puppies need to be taught not to jump up on humans as this behavior will manifest into other meanings as the puppy grows up into an adult dog.
Many puppies don’t know their strength. When they jump up and you wave your arms and try to push them off, they may think it’s a game and grabs and bite harder. Tell them it hurts the same way another puppy would, with a YELP! Lay it on thick, overact and cry and sob like the pup has done major damage. Some tough dogs get the message using this. For the out-of-control grabby, ambush type of dog play, give him a taste of his own medicine and SCREAM (very loud but very short), and fall over “dead.” Don’t move and don’t say anything. Play dead for at least 15 to 20 seconds. The shock value may be enough to send a permanent message that such games stop all interaction, plus they hurt you—and playing dogs aren’t interested in hurting you and won’t want you to cry.
Why do dogs jump up? A plausible explanation arises from their ways of communicating with each other. A puppy greeting an adult dog often licks the adult’s muzzle -- a polite, deferential behavior. Dogs, of course, descend from wolves, among whom muzzle-licking is how pups get the grownups to regurgitate food for them. Domestic dogs rarely nourish puppies this way, but muzzle-licking has survived, maybe because deferential behaviors are handy for a social animal. Think of humans saying “No, after you.” Muzzle-licking is also an appeasement behavior -- something you trot out to de-escalate a fight. A human might lift up his hands, palms toward the person he’s arguing with.