I think it's fair to say that a gun is a far more efficient killing tool than a knife, and if any person wanted to kill you they would choose a gun over a knife.

Irrelevant. A threat is a threat is a threat. A knife maybe less effective, but it is still effective.

If I'm not mistaken one of the rules for owning a gun is something along the lines of "Do not point a gun at anything you don't intend to destroy". So in your scenario you are introducing a firearm to a potentially empty threat, you are escalating the situation.

If it's empty I would not draw. Why? It's not a threat.

"I am going to punch you" can be a viable threat. I agree that it has to be presented as a viable threat. Even if you don't intend to punch me but present it in a way it is perceived as a viable threat then do what's necessary. Even if it means deploying a firearm.

It is true the person created a violent situation, but you are escalating it by introducing a gun. There is a world of difference between the threat of a punch and the threat of a gun and you are bringing it to a potentially lethal situation.

A punch can be deviststing. A punch could lead, death, hospitalization, CTE. None of that I or anyone would want anything to do with. It is perfectly reasonable to defend yourself against such a threat, with a gun if necessary.

Even if threatening to punch someone is different from threatening to kill someone. You have crossed the threshold in with self defense with violence is justified, which is a threat if bodily harm.

Yes but it's harder to kill someone without a gun.

Doesn't really matter. I can still be killed if you are unarmed.

If neither person has a gun then the chances of a casualty are reduced significantly and that to me is the ultimate goal, to stop killing each other.

My goal in a self defense situation is to stop the threat. This is not about "ultimate goals" this is about yourself in a situation where bodily harm is a threat. Some threats required the deployment of a firearm.