The only time dogs “hug” each other is when the male clasps the female during sex or when a dog (male or female) mounts another dog in a dominance display or in play with familiar dogs. If one dog reaches a paw over the neck of another in the first seconds of their initial greeting, he’s pushing the socially acceptable boundaries of canine good manners. A “paw over” is the precursor to what’s called “standing over” in canine ethology, and it’s done in the context of establishing the social hierarchy. I do see dogs use it in the first second or so of a greeting, but they’re not necessarily
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