Hello
I think timing is a key here. I carry a knife , being a Silat and Pekiti Tersia Kali man....so, all that needs to happen to potentially cause a knife vs . knife incident is for someone to show up with a knife and one of us ...I assume in this case, my attacker, has a knife out and (hopefully)mine comes out. When it comes out ( if it does) is a question of timing ....can I disengage with distance and get mine out? Can I get mine out fast enough to be ready for the attack before it is initiated? Do I have better options than my little tactical folder ? Do I , sensing something is amiss, go ahead and discretely deploy my knife, then find out this guy has one ? etc, etc...... Ideally ,Knife vs knife training should be more conceptual in nature . Really, it is more of : he has a short weapon vs I have empty hand or a short weapon as well. His hand could have a knife , box cutter, sharp pencil, bottle , tent post,screw driver , carpet cutter, etc and you have a knife or empty hand ( or a pen, ashtray, mag light). The routes of motion , ranging, footwork , body positioning , etc. you train through should all presume the knife is present regardless of if you see it or not. The hand manipulations , deflections , etc, should not be so vastly different from your empty hand vs, knife or empty hand vs empty hand work. Then ,"knife in hand "work merely addresses the unique considerations of that weapon bearing condition. Ultimately ,the drill trained needs to be transferrable to weapon vs empty hand and empty hand vs empty hand variants of combat situation. Since, knives have to be dealt with not necessarily with a knife in hand ....and the knife may , more often, be employed in other situations, a good knife program should not dwell exclusively on the actual "knife to knife" situation. Perhaps , the problem with a knife to knife focused program is it is a unique system being attached to another /other unique hand fighting system(s) and other weapon system(s) that all use different principals and movement patterns rather than having a core system that transfers to all combative situations.
Knives are everywhere ,as are other potential weapons. Everyday, as workers visit my clinic or people disrobe to have a physical , I observe tactical folders ( as well as screw drivers, box cutters, etc....). Its not like knife and "knife like " weapons wielding people are few and far between. If one of them pulls out a knife , since I have one as well....we have all the ingredients for "knife to knife". I just have to get mine out....and that is hard to predict if it could or would happen. No one can say with certainty until after the fact.The question again is "timing" and also "situational pressure". If I would manage to get my knife out ...perhaps ,because he drew his to threaten more than attack, and I use that hesitation to get mine out....now we are starring at each other with knives in hand .....now the question may be in "will to fight" .
Knife on knife fights do happen. Consider that people do not fold and crumble from immediate shock when hit with a knife, so the notion that because you are hit, your knife won't come out is innaccurate. Perhaps ,what people find hard to imagine is two people with equal blades lining up on each other to "duel" as if they are in a Tae Kwon Do style sparring match with knives substituted for kicks and punches.There are a lot of possible scenarios. An "ambush " style attack ,of course ,leaves you way behind in time and your knife may very well never deploy, but the response patterns practiced with the knife in hand may still be able to come out if you realize what is happening AND your training has emphasized these responses to be valid with OR without weapon in hand.
I think it would be hard to catch these sudden explosions of violence on video tape. I've seen the results of real world ( yes they do happen !!) knife on knife encounters in my ER. My first one was amusing . The young lady felt she was the "winner". She told me this as I was repairing a long laceration on her forearm.......and getting ready to repair her facial wounds. She told me her opponent , another young lady, had a pretty cheap knife ...when it hit her forehead the blade broke on the skull...she took that opportunity to seize her and drive her knife into that girl's abdomen.
The results are often not for the squeamish or faint of heart.
With Respect,
Doc D
dropped his and ran away real fast. 
