He and the other will start fighting if the other dog comes close to the bone he stole.
Resource guarding is common in dogs, and stealing is just a bullying behavior, like a bigger kid on the playground taking over the swing just because they can, even if they were more than happy to play on the slide until someone else started using the swing set. If they get away with it, the dog is rewarded by a new tasty bone to chew, and if they learn which dogs will and won't put up with their bullying. My dog does this occasionally (she normally waits until a dog is distracted and leaves the bone for a second, then takes it and won't give it back). She knows the 'drop it' and 'leave it' commands, so when I catch her either taking something away from another dog, or starting to act defensive about having it (like tensing up when another dog walks by, acting to cover up the resource with mouth/paws, or giving whale eye), she has to leave it alone, and she gets rewarded with something else for choosing to walk away.
If there's ever a question that one of the dogs will escalate to snapping or biting, remove the items of contention completely when the dogs are together. Guarding is an anxiety problem, where the dog fears losing something valuable. The more they feel that fear, the more they feel compelled to act on it, even if no real threat is present. Like people, dogs don't learn well when they are anxious, so you have to remove the anxiety in order to teach them what you want them to do. The dogs can both have the bones while they're separated or crated, but they need to be put away before allowing the dogs to interact so no one becomes anxious and defensive.
Thank you Laura, I was kinda thinking that and instinctually started the counter measures. My 3 year old 17 lb spaniel mix bullies a 9 month old 50b pharaoh hound. That baffles me, sounds like anxiety and fear for sure because the first time they met my dog froze with fear and then went into fight mode when the dog came closer. My dog is generally more on the anxious side through. He was a rescue and I have had him for about two months. Thank God I have figured which one to move away to diffuse a situation and they generally get along now. Thank you for your response.
It's definitely not about size. Dogs don't even seem to notice size differences when one is more assertive than than the other, and humans often inadvertently reinforce bad manners in smaller dogs while encouraging bigger dogs to just put up with it. Small dogs often get away with worse manners because they're 'cute' and 'harmless' while bigger dogs can appear much more threatening when exhibiting the same behaviors. Bigger dogs often get scolded for 'being aggressive' when they are really responding appropriately to bullies (like giving them warnings to back off and respect their space), which reinforces the bullying behavior in the smaller dog because it's now been supported by the human.
4) Now We’re in Trouble, Part II: Dog B is socially inept – Dog A is chewing on (insert valuable resource). Dog B approaches. Dog A gives “the look.” Dog B is oblivious, and keeps blundering forward, until Dog A feels compelled to escalate the intensity of his message, to aggression if necessary, to get his point across.