"I then chose to have a chat to find out why". My point exactly. I would have left it there. You had made your feelings plain enough before then. Anything else is just a waste of time. Do you really think that having a discussion (read argument) in the middle of the road would make her understand any better?
Yes, you would have chose to leave it there, I didn't and don't. Different courses and all that. As for waste of time, maybe not. She wouldn't back down or admit she is wrong at the time. Not many do. However, what a situation like that does, is make you think. I'd bet she'll drive slightly differently next time. I'll bet she'll give the next cyclist a little more room, if only to avoid further confrontation. Some might argue that she'd be more agressive next time. I don't buy that. No-one really want to hurt another person.
What evidence do I have for this? None of course. But then, what evidence do you have that it will make no difference and be a waste of time?
Looking more generally, do you agree that inaction leads to status quo and action can make a difference? I certainly know that a lot of people don't like what I do, but I'd hazard a guess that I have made a difference. I have made some people re-evaluate their attitude/driving/cycling etc. Did I do this by accepting my lot, or taking action?
Sure if I have made a difference, it may be small, but I think it is a difference. Lots of people making small differences....