I understand what you are saying and I agree with the first part. However being calm and collected is only really valuable in connection to good wits and having the introspection to be realistic in your assessments of situations. I've seen a calm person get knocked out, and the calmness did that person no favor; fear might have helped there. A little bit of fear can be a healthy indicator.

Everyone needs to understand that they are not immortal and they are simply not in control of everything, and that they should react accordingly to situations where you can see potential harm. Arrogance can kill, and we're talking about a person saying things like "I'm the only adult woman I know that's not afraid to walk to her own car at night. Like, you think men are scary?". I think you make a good point but that woman needs a virtual reality check before it's going to be a real life reality check.

Besides this I personally think the reason she reacts the way she does and reads as negatively as possible into my comments is that she does not take criticism well, which often goes hand in hand with arrogance, and deals with it by marginalizing the worth of my point and mocking me.