Almost all puppies play bite. They do it to other puppies, to adult dogs who'll let them and to their owners. It's important to distinguish this constant biting from bona fide aggression, where a dog threatens or bites when guarding his food, when uncomfortable about someone touching him or when uncomfortable about strangers coming too close. Aggression is less common in young puppies than in adult dogs but is not unheard of. If you think your puppy is showing signs of aggression, get yourself into competent professional hands. Many kinds of aggression can be resolved.
The reason puppies play-bite so much (it is their main activity aside from eating and sleeping) has to do with their ancestry as social carnivores. Wolves and wild dogs are equipped to bring down large prey animals and so must have extremely strong jaws. And, in close social situations, there will be arguments and competition over food, resting places and mates. During these day-to-day scuffles, it's vitally important that dogs not use their full jaw strength on each other the way they do on their prey. Instead, they use ritualized aggression—threats, body postures and inhibited bites—to settle arguments.
The ability to bite without maiming force is rehearsed in puppyhood during play biting. Puppies are programmed to do it so they can learn about their jaw strength. When one puppy bites another too hard with those needle-sharp teeth, play grinds temporarily to a halt, which provides a potent consequence to the biting puppy. Over time, the bites become consistently gentler, in order to keep play going. Without this constant feedback about their jaw pressure, puppies are at higher risk to grow up without acquiring the capacity to inhibit the force of their jaws.
The best policy for owners of young puppies (age 6 to 16 weeks) is to allow play-biting provided it is not too hard. Hard bites should result in time-out penalties—cessation of play (leave the puppy alone or put him in a "penalty box" for a minute)—as consequence. Only when the puppy has gotten reliable about biting more softly should play biting be phased out altogether, by re-directing the puppy to toys and giving consequences for all bites. This way, the dog has a much better chance of growing up with good bite inhibition. Free-play with other puppies and friendly adult dogs is another good forum for puppies to develop bite inhibition.
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