I mean it seems kind of obvious to me but maybe in over simplifying things...
3 scenarios i can imagine. Someone comes into your home with the intent to have an argument... (Someone you know most likely according to that article), scenario 1 no gun is present and the argument happens old school
Scenario 2 you have a gun but the other party doesn't, there is a struggle and someone gets hurt, it doesn't matter who gets hurt, it's probably serious. Same could be true for knives but potential for damage is probably less.
Scenario 3 you both have a gun, you raise yours in protection and that very act causes a potentially fatal gunfight. How many knife fights do you hear of? Even near London I don't hear about them. You might hear about the use of a machete sometimes but that's the closest.
I'm sure there are scenarios where everyone is safe and others where the gun did indeed act as a deterrent i just don't like the odds when firearms are involved.
Btw, my knives all have points, much to my fingers detriment!