Hi Stillhealing!
I was a bit sad to hear about your story. I can relate in some ways.
For me, leaving therapy and interacting with "regular people" again is the best thing that I have ever done. It was painful to realize that it was of little or no use to me, even harmful (I had a thoroughly incompetent and abusive T)
But I do believe that T's do not possess any special knowledge that is more useful in becoming a full human being than any other insightful or aware person on this planet. This whole "projection" thing that you mention would drive me crazy; it's basically circular reasoning, and is not supporting his theory with actual logic, just repeating the same premise.. that it is YOU and not him. You have provided some concrete reasons for your fears, and logically, either A. He really is busy and should inform you what his policies are on guaranteeing time slots so as to prevent any further misunderstanding. Unilateral decisions on his part need to be explained. B. He has other reasons why he keeps rescheduling your appointments, and you deserve to know why. C. You really are projecting a fear of abandonment, but based on actual changes in his behavior, which seem incongruent with his words. For now, it (your projection) is only a theory. The fact that he keeps repeating it or saying "because I said so" does not make it valid. He is an "expert" in psychology, but you are the expert on YOU. By the way, had he said "Do you think you might be projecting".. as a respectful means of encouraging you to become even more aware, more of an expert on yourself, that would have been an entirely different matter, I think. But only if he was honest with himself and asked himself the same question.
There are books one can read about these mind traps. The more you try to defend, the deeper you will get drawn in. I suggest just repeating the same question over and over again if your T keeps evading the original question, but keep it simple, straightforward, logical, respectful, and objective. Repeat the same short question over and over again until you get your point across instead of becoming more ensnared. For example: "This is the third time you have cancelled or asked to reschedule my appointment this month. Why?" The point is not to keep asking till you hear what you want to hear, (you may very well not and have to accept the answer) but to NOT allow the person to evade or deflect the original question. It keeps the discussion from being over-controlled by the T, and allows you to feel balanced and centered. You need more data in order to assess why you feel the way you do, and most likely don't want to give him a reason to view you as feeble-minded, which I'm sure you are not. Respect yourself, and he may begin to respect you and your thoughts, ideas, and perceptions.
I'm very glad that I was in therapy to see what it was like, and I learned a great "negative" lesson, and grew in unexpected ways. In the end, I discovered that the most important person you can love is yourself. I really do hope you find that. It's not going to be found with a T. This much I do know. Easier said than done, however.
However, if you decide to stay, I agree with LL. Trust yourself. I am very bothered that anyone would tell you that your perceptions, thoughts, and feelings are "incorrect". Don't let anyone define you. Suggestion: call him on it with the same respect you would show any other human being, but call him on it. Sounds like he is fairly certain you are not going anywhere, and people often do behave strangely when they know you are hooked. Tell him that his words and actions, to you, don't seem to be in alignment. This would be distressing to ANYONE, in therapy or not!!
As far as "running" goes, maybe you had good reasons to in the past. (or not, I don't know) I have reinstated my "3 Strikes" rule and am more than willing to walk on the third strike. Of course, I'm talking about major transgressions, not minor misunderstandings.
Oddly, as a result, I have been less likely to become a "victim"... I don't attract people that abuse power because I am firm about it.
The key is honesty. Sometimes people grow apart at different rates. It happens in real life, and it happens in therapy. But therapy, at times, I think, is inherently dishonest. It can be useful, yes, but it is my opinion that one has to suspend their disbelief in order participate in therapy, and to me, and many others I know, it just feels off. Nothing lasts forever, enjoy the moment while it lasts, but know when to gracefully exit any relationship that outlives its usefulness instead of trying to force something that just isn't there anymore. (My opinion, based on my own experiences...I'm not saying it's time to exit, only YOU know the answer)
Hope it all works out, and that somehow you get something out of it.
People here are rooting for you. Love yourself as well!