Hi. I'm a Former Marine and practitioner of the proprietary "MCMAP" art, Aikido, Judo, parkour, and others. I've been in many fights, subdued people in violent real-world situations, been shot at, stabbed, etc. I feel "comfortable" in hostile environments at this point, at least to the degree that reason and preparedness allow.
I've come to the conclusion that there are a few major factors that apply in any of these situations, and having a knife or being able to throw a flying dragon kick is not one of them. First, you have to know when to fight and when to avoid fighting. This is simple: 99.9% of the time, you avoid fighting. There's nothing cowardly or unmanning about that. It's just tactically-sound advice. Unless your life is in imminent danger (or you're willing to risk your own life in the defense of another person) fighting should not even be part of the equation.
Another thing is escalation of force. A lot of people who carry weapons don't understand this concept, but producing any sort of weapon is an escalation of force. A shoulder bump can quickly turn into getting shot in the face if you pull a knife, and most people wouldn't blame the person who shot you. Knives are brutal weapons, and even LEOs are trained to respond to them as an imminent threat to their life (i.e. you're probably going to get a hollow point in the chest if you pull a knife on a cop.)
Martial arts won't help you. Even if you practice long enough to make use of a move or two, what is your plan? Use an arm-bar TD on someone who bumped into you? You will probably be swarmed by other people so fast your head will spin, especially if you bust out some judo on a woman who appeared to be just walking around.
Fear is a natural response to threats in your environment. Anyone who isn't afraid of someone bigger, younger, meaner, etc. who is posing a threat is probably quite dumb. It's not a matter of shame, it's a matter of sense and survival. It's nature. The only thing training does is drill into you the ability to operate in spite of that flood of complete terror. It allows you to continue making rational decisions quickly enough to (hopefully) survive.
The first of those rational decisions is usually "can I get out of this without putting my life on the line?" And in most "street" confrontations, the answer is yes. Walk away or avoid the situation altogether. Some punk tough guy (or girl) on the street is not worth worrying over, much less initiating an exchange of violence.
Note...I used to date one of those hypothetical IDF-trained women that were mentioned. I'm not even sure I could have taken her down, knife or not...so you don't want to get on their bad side lol