It looks like an earlier post of mine got lost in bandwidth trouble.
Basically I did not understand the point of the video showing a dog, owner, and red sock.
What is the purpose of training a dog to hold on?
It depends on the purpose. Smaller dogs are trained to hold on because they get down into the burrows of smaller game, and the hunter can get the game out by pulling the dog who's holding on to the prey. For other dogs, they're trained to hold on but not damage the prey, bringing it back to the human to dissect (or take to a taxidermist) themselves. Still other dogs are trained to hold on in order to drag a target off its feet, or in the case of protection/police dogs to subdue a target by pulling them to the ground. Bully breeds had two main purposes: to grab a bull's ring (in the nose) and hold on no matter how much the bull thrashed, or to basically grab on to game like a boar and hold it while other dogs or a human caught up and finished it off. Almost all dogs still have the instinctual habit of grabbing and holding a target, then giving it a "kill shake" which results in a broken neck or back depending on the size of the game and the size of the dog-- wolfhounds (Irish wolfhounds, borzois, Afghan hounds) tend to display this behavior most notably, but the larger mastiff breeds do as well (along with crushing grips for the latter). I posted a National Geographic video a page or so ago where you can see different dogs doing this toward a human subject (wearing a protective suit), and see how each uses their size and build while holding on to the target.
Regarding "The stick", what is the track record for getting dogs to let go of humans by inserting thumbs in the eyes? (sure, it's cruel, but if it is holding on to me I will not be in a nice mood)
Gouging eyes is likely to make it start snapping, and if what you're looking to do is end the attack without saving the dog there are other ways to accomplish it. Dogs are just as susceptible (more, actually) as humans to a knee to the chest, or even more painful would be a blow to the nose-- dogs have an order o magnitude more nerve endings there than humans do-- so the heel of your palm into the front of the nose of a dog is going to hurt far more than the same done to a person, and could shock the animal to release and reel back. If you're attacked by a dog and are afraid for your life I suggest raising your weaker arm in front of you horizontally (to keep it from aiming at your head/face/neck, and if it grabs your arm be ready to bring with all the force you can muster your knee into the front of its chest (below the neck) or directly into the sternum, whichever is easier.
Also, please note that none of this is any kind of official instruction on how to fight off a dog attack, nor is it to imply in any way that these are techniques I would use to separate dogs that are in the middle of a fight. This forum is not an adequate environment to teach defensive techniques and my post should not be taken as a lesson plan (no "specialists" or "special technique" being trained here). If you're concerned about possibly being attacked by a dog then carry mace and
see a veterinary professional for the best advice.
The takeaway you should get from what I'm saying is that a pit bull is a dog, and has dog physiology, and no amount of tenaciousness is going to change that. Inflict severe damage and yes, the dog will let go.