When I first started thinking about knife defense, I went through a lot of this in my head. I had the advantage of starting with knife dueling according to 16h Century methods, so I knew first what knives were used for, as well as using the off-hand for parrying, trapping, and striking.
Basically what I came down to was this:
A knife is stronger than empty hands, period. If that weren't the case, it wouldn't be a weapon. I don't cut my steak with my fist, it's not suited for it.
Training is an important factor with knives. Just owning one doesn't automatically mean you're dangerous. The more you train with it, the more efficient it becomes as a weapon.
Starting from these two often-forgotten conclusions my answer became simple.
(Obviously these conclusions are generic, anything could happen. I know someone's going to argue that point anyway, but I felt like stating it now so I could simply copy and paste it again as an argument for later.)
A.) A trained empty hand fighter generally beats an untrained empty hand fighter.
B.) A trained empty hand fighter is as equally equipped as another trained empty hand fighter.
Now, up to this point, most people keep their common sense. Hopefully, most people realize that there is no "magical" style that will guarantee victory against anyone else who has trained as long as you have. If you go into a fight with an equal opponent, you have 50% chance of winning.
But, you add a knife (and, curiously knives seem to be the only weapon that does this to people), and that idea of common sense goes out the window.
A knife can equalize the disparity in training. So:
C.) A trained empty hand fighter is as equally equipped as an untrained knife wielder.
--This means that defenses against an untrained knife fighter are about 50%. Bad odds, when your life is on the line. Especially when the "edge" is with the house on at least needing stitches.
D.) A trained empty hand fighter will lose to a trained knife fighter.
I don't see what's so hard about this. If you're equally matched before he had a knife, why do you expect an advantage now that he has one (and is trained with it)? Does a knife make it harder to fight all of a sudden? But that is what many "knife defense" enthusiasts claim. I even saw a quote once, supposedly by Bruce Lee that went something like: "An empty hand fighter will win against a man with a knife, because the empty hand fighter has four weapons, while the knife fighter only has one." (Ha! Apply that saying to a shotgun, and see how much sense it makes!)
:bs:
It's quite simple, to me. As hard as you train against knives, as long as you are limited to empty hands, the best you can hope for is to even the odds against an untrained knifer. Which is worthwhile to me, so I train for that.
Of course, why would I get into a scrape with a trained knife fighter in the first place? Besides, "trained" fighters usually get you before you even know they have a knife, so the best defense against them is being aware and alert.