You are not required to brandish a weapon because this isn't a thing you should do outside of a movie. Waving around your gun means someone takes it from you.

This is even more laughable with a knife.

I'm not defending anything except my position that your assertion is incorrect. Brandishing a weapon with the intent to scare someone off is illegal in its own right in every jurisdiction I am familiar with in the US. You are giving bad advice and you need to educate yourself before you give what could be interpreted as legal advice.

You are defending someone

Most of the people here are rebutting your general claim that self defense is only available to the unarmed. Those rebuttals don't constitute support for this woman.

If you are armed you can force them to leave through threats

I am making a general comment on your argument, and not specific to this case. Like most of the arguments directed at you in this thread, My comments should not be construed as support for this woman in this particular case.

You are conflating "threat" and "force". They are distinct. A "threat" is an attempt to influence the subject's decision to act, by making them fear a future action. "Force" is a physical action imposed on the subject.

A threat is something intended to convince the subject to decide to act in a particular way. Force is when the subject's choices are removed, and their body is physically manipulated against their will.

Force can also be a threat, but a threat alone is not force. Holding a knife to your neck and demanding your wallet is force (your neck is being physically manipulated against your will) and a threat (you are being coerced into giving up your wallet).

There are six generalized criteria for defensive force. A person who 1. Reasonably Believes an imperiled person faces a 2. Credible, 3. Criminal, 4. Imminent, 5. Sufficient threat (sufficient = "death or grievous bodily harm") may use any level of force 6. Necessary to stop that threat.

When you articulate your arguments about this specific case using the above terminology, you will find that your opinion is shared by the overwhelming majority. There is very little support in this thread for her self defense argument.

An armed person theoretically has a greater capacity of force than an unarmed person, but threats made be an unarmed person can certainly justify a forceful response by the armed person.