Bacteria that normally cause no issues or are even beneficial can quickly become problematic if they gain access to an area that they're not supposed to be in. Your body isn't really familiar with these bacteria in terms of immunity because they aren't typically present in areas where your body is able to recognize and identify foreign antigens. If you think of your mouth/digestive tract as one continuous tube separating your insides from the outside, the bacteria present are really on the "outside" of your body. With bite wounds, suddenly these bacteria have access to deeper tissues and potentially even the bloodstream. They're completely foreign to these areas, and there aren't any normal flora present to compete and keep the new bacteria's population in check. Only now can your body start to recognize them and fight them off. I'm not sure about mouth flora specifically (of which composition can vary greatly), but plenty of bacteria have adaptations that specifically help to protect them against our immune response. Once they start proliferating where they don't belong, our immune system is usually in for one hell of a fight. There's good reason that antibiotics have become such an invaluable tool in modern medicine. Some of those little fuckers are tough, and they've been learning to fight back against our defenses for millions of years.