My reaction also was SHOCK at reading your post. I would feel just as devastated as you do. The conversation strikes me as very strange from her end.
No doubt in my mind that she reacted badly. It sounds like she was very defensive. She may believe that she was honest with you when she said it's normal for private practice t's to cancel alot, but I don't think it's true. My t isn't private practice, but i will tell you that in 10 years, she has only cancelled a session 3 times -- always for something major and unexpected (her house burned, sick child). I disagree with her that your counting the number of times she cancelled is unusual. I would have done it myself. As other posters have said, many of them still remember how many times their t has cancelled on them (so they also counted).
I think your t exaggerated what you were asking for. You kept telling her you just wanted a little more consistency, but she insisted you wanted "absolutes." I didn't see in anything you wrote that you wanted absolutes. I think the type of conistency you need is very normal and necessary and something that most other therapy patients expect from their t's. Not anything out of line at all.
As far as trying to understand why she was acting so strangely (you said she's never been this way before). . .I wondered the same thing Rainbow did. . .whether your t (or someone close to her) is ill. It would explain only why she'd be taking 3 weeks of personal leave. Also, if she's worried about whatever is going on, she would be more likely to be emotionally reactive and behave in ways that aren't normal for her. It would also explain why she has cancelled so much, and why she says she can't guarantee you consistency now.
I also wondered why she was taking on more work in addition to her full-time job. Again, this could be because there's some medical crisis going on in her family, and they need more money.
It doesn't excuse what she said and did -- but it might be an explanation.
The important thing in my mind is that, for whatever reason, your t cannot provide the consistency you need. I think this much is true. She has already demonstrated that by cancelling 8 times. Considering that she is going to be working full-time + 2 nights a week, she is going to be very busy. She has made it pretty clear that the inconsistency will probably continue, and she also recognizes that this is probably not what you need.
As horrible as this experience has felt for you, it's good you found this out now, only 6 months into therapy with her, rather than a couple of years down the road when you were even more attached to her. Unless you think that you can tolerate this continued inconsistency, and her defensiveness and poor reaction to being questioned, i would suggest you seriously consider finding a new therapist. I know how hard it would be since you already feel somewhat attached. But you are likely to find someone else that is better suited to your needs, more consistent, and who you will feel happier with in general.
I'm so sorry you're going through this. . .

I can just imagine how it must feel.