I'm gonna dissent a bit here. I view my dogs as a critical aspect of our overall security. I have a Chihuahua (yup) and a mongrel that looks to be a retriever/spaniel mix. The Chihuahua (Goliath) obviously won't engage in conflict but he is quick as hell to determine if someone's lurking or entered our yard. Thankfully, he only makes a racket when he thinks there's trouble. He's an audible component. The rescued mutt (Shadow)is fearless, tough as nails and has twice sent an "intruder" (both times were my brother, who's a brawler, barging in unannounced) running back outside with blood streaming from torn up legs. Neither has a minute of training (I haven't even taught them to sit on command). I won't leave guests alone with my kids and Shadow. He is VERY protective of my three girls and won't hesitate to f^*k someone up if he feels that they're threat to 'em.
That still doesn't mean he'll stick around to protect anyone if someone inflicts a serious amount of pain on him. He's probably never been kicked in the head (at least let's hope not). Most dogs will go into avoidance when placed in a new/stressful/uncomfortable position, which is different for every dog. It could be that a new guest that they don't know sends them running (which is definitely NOT your dog), or it could be something as extreme as a boot to the head. A dog with a strong fight drive will come back twice as hard, pain and stress escalate his willingness to stay and fight. This is probably more dependent on genetics than it is on training, which is why you see certain types of dogs used for police/military/protection work.
I'm not saying your dog won't stay around and protect you, but unless he's been trained to BE in that sort of situation, you certainly cannot count on it when things get hairy. Realistically, if he bites a burglar in the leg when he's climbing through the window, the burglar is probably not going to stick around and fight the dog. Only crazy people stay and attempt to fight a dog, but those are the ones you need to worry about. Additionally, the dog needs to be taught how to bite. In a bad situation, you don't want him doing quick bites at someone's leg, you want a good full bite on the arm to subdue the bad guy.
Also, if you haven't done any training as you've said, then you need to. If the dog is so quick to bite, and has bitten your brother, then he's a lawsuit waiting to happen. If he bites a neighbor kid for some reason, then you'll be lucky if you don't lose your house over it. I know a couple of people whose dog bit someone for no apparent reason, trust me, you do NOT want that to happen. My brother had like 200 stitches in his face from a Yellow Lab when he was 4, and my wife had over 100 in her leg from a german shepherd. It can happen in 1/4 second, before you even have time to realize what just happened. Those were both *ONE* quick bite, not multiple bites. It's just like having a gun in your house, it's there when you need it, but you don't leave it loaded sitting on the floor in the living room with the kid's toys. Obedience isn't just about teaching to dog to sit and stay, it's about teaching the dog the proper way to behave without you having to tell him what to do all the time, and also that it's not okay for him to go off like a loaded gun when someone walks through the front door. Not only would you feel absolutely terrible if the dog bit a friend or neighbor, but you'd probably lose everything. Even if they didn't sue, insurance companies WILL sue to recoup certain costs.
Sorry to get all lecture-like towards the end. I've had, and been around german shepherds my whole life, many of them protection trained. And, I've seen firsthand what happens when a dog bites, and what sort of behavior/training (or lack thereof) leads up to it. If you have a dog that will bite, which yours will, then he needs to get some training ASAP to help mitigate the risk of an accident.
