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.
An anxious or playful pup may leap high quickly and suddenly “poke” at your face with their nose. That can be triggered by leaning over the top of them especially when they’re in a high-arousal situation like a homecoming or around other dogs. It may be a way for stressed pups to relieve their anxiety, so be aware of situations that cause these behaviors. Dogs control each others' movement with their body language. Think how a Border Collie makes sheep move just by getting close. You can stop your pup’s jumps by stepping close to him just before he leaps. Cross your arms and step into the pup’s personal space before he crouches to leap.
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.
Unless given a command to jump, a dog should never be allowed to jump on humans. A dog that jumps on humans of its own free will is a dog that does not respect the person it is jumping on. Even those cute little toy dogs should not be allowed to jump on people. While you may think it is cute, it is not cute to everyone else. Not only is it annoying to most people to have someone else's dog jump on them, it can also be dangerous. A jumping dog can knock people over, muddy their clothes, put runners in nylons and scratch the skin.