johnnyghost,
dog-dog aggression in the pit bull is possible and sometimes <again, sometimes> common. There is a range of tolerance levels toward other dogs. Dog-dog aggession does-not- translate to aggression to people as it seems like you know, but many people in general do not.
Little dogs can be aggressive toward people because they often are carried around and hidden in bags and strollers, with no opportunities to actually act like dogs and experience the world. Lack of experience creates distrust, which can lead to fear. Fear can lead to aggression. Little dogs also are more likely than bigger dogs to perceive people as looming giants doing strange and stupid things with and to them, and so will become fearful.
Many people also excuse the actions of little dogs as "cute", over-protect them. An/or transfer their own anxieties onto them, through how people react with the little dog <pressing their little dog against their chest and acting worried about another person or another dog will create anxiety in that little dog and over time lead to a fearful response by the little dog>.