Ah, this is a very perfect example of DBT's wise mind processing......T says he needs to cancel & reschedule on Friday.....emotional mind really gets hurt, feels rejected, hurt & abandoned by those you need around you for the support you were so desperately needing at that point in time.
Step back, look at the big picture & T's side of the picture as Chris explained.......allows the rational mind to start working & seeing the whole picture rather than just your emotional mind's thinking.....&
Radical acceptance.....appointment changed to Friday & logical thinking.....He was definitely not going to be all there for your appointment to give you the support you really needed so what he did was best for him & also for you.
The emotions you felt were definitely valid for the situation.....know we all feel some disappointment & hurt when things don't go as we need them to especially when we are having a bad day to start with.....but sometimes we just have to accept what is & make the best of it & know in our logical mind that it's really the best thing for the time & you will be able to make it until Friday.....it's only a few days away now.
Sorry it happened....I know that the stress is causes & it's a bit short notice when you were already at the office....usually they give the same respect that they expect from us......24 hrs notice

It's not like he does this all the time....so at least you don't have a real flaky T that you are dealing with.