First part. Why should you not carry a knife for "self defense". Well, as someone who studied knife defense and knife attacks, there are many reasons. Bottom line is, it's just not efficient. Knife attacks (defensive or offensive is SLOW)
Are you confident enough in your "knife skills" that you will be sure they will not take it from you if things escalate to such levels? A knife wound is most likely fatal but it isn't instant and doesn't have stopping power that a firearm has. If you read accounts of people who have been stabbed in confrontations, you will always hear that they initially thought they were being punched over and over. After the 30 second ordeal, they see a pool of blood and realize there is something wrong. How much damage can you do with a knife against ONE GUY to stop him from doing whatever he is doing (assuming he is intent on hurting or killing you)? A lot. How long does it take? FOREVER. (relatively speaking) And you have a knife against multiple people, it's not going to stop your head from getting smashed in. "2 guys in a knife fight and both will end up dead."
I will give you the deterrent or "intimidation" incentive. There are 2 problems with that. So, when do you pull the knife out? Because if you pull one before the "attackers" or "trouble makers" pull one, you just escalated a situation from what possibly could have been a simple, "give your money and leave" situation, to a possible life or death situation. I don't know about legality in your state, but you cannot brandish a weapon like that or you're looking at serious time. Unless you feel your life is in danger. Which brings me to the second scenario:
They pull a knife or some weapon on you, or THEY escalate the situation first to one where you feel your life is in danger. In this case, you pulling the knife makes sense if it's all you have. It will be intimidating. But wait, oh one of the guys has a gun. Or 3 of them have knives and one has a bat which has a longer range and they feel challenged. They're angry you would even attempt to challenge them, you don't look confident. You look scared. They can take you for what they came for and because you tried to be a hero, they're gonna teach you a lesson.
A knife is just as illegal as a gun if used improperly and just as much of an escalator as a gun, without the instant stopping benefit. I can go on man, I've studied knife defense to know that there's only a few things I know about knives. Knives are no joke, run whenever possible. If studying knife defense teaches you anything, it's that there is no 100% foolproof method of defense and that means you wielding a knife is just as much of a danger. It can be stolen.
I'm not going to even go into the legality issue, timing, range and just the general shortcoming of a knife. If you're going to carry a knife to feel better and empowered walking the streets, then you are sadly mistaken and do not know the reality of knife attacks. (by you, i'm talking generally not addressing eric)
The second part, I don't understand the logic. You're basically saying that having a knife as a deterrent and being the primary aggressor is so intimidating that they would not challenge you, therefore you don't need to know how to use one? You are banking on the fact that they will not challenge you. As I wrote above, I don't know if you're picturing some college town with some douchy frat boys stealing beer or something but I'm talking thugs in a bad neighborhood. You would be lucky to get out there alive with a GUN if there are more than 1 of them. Wielding a knife that is barely an extension of your striking range against multiple attackers in such environment is absolutely suicide. It's a challenge.
Frankly, you can know how to use the knife like it's your 3rd hand and know exactly where to cut on the human anatomy to disable an opponent instantly and there is still the issue of legality. People who haven't studied the legal ramifications of such attacks and encounters have NO IDEA how your life can be completely ruined because of ignorance of the law. The reason why I don't recommend knives as self defense is because most people carry those $20 home defense big5 clip on knives and naively feel empowered and yet have absolutely no idea what comes after an encounter.
Cliff notes: Don't be a ****ing hero. Give up your money and live another day. EVEN If you are armed. If you are going to be armed, don't choose a weapon (aka knife) that is...1) just as illegal as a firearm, 2) perceived as more gruesome and violent to the jury than a firearm, 3) doesn't give you the range and distance extension of a firearm or pepper spray, 4) doesn't incapacitate and STOP the aggression immediately.
I guess what I'm saying is if you're going to be armed and want to do it right, get a firearm and do it right, legally and train your ass off so you know how to use it safely, properly, and you don't injure someone or yourself. Or carry pepper spray which is $10-20 and has hardly any risk in using it.
And if you do happen to be jumped one day, just give them the cash in your wallet straight up. Perhaps if you've been mugged more than once it could be worth getting something to defend yourself, but that hasn't happened yet. It's not like muggers particularly want to kill or harm you - They want your cash-money. And if you have to give up the $100 cash in your wallet once one day in the future, is it really that bad?