I do not think you are being unreasonable at all. I would feel the same way you do. If their proposed time doesn't work for you, then it doesn't work for you.

I can be very very passive aggressive in situations like this. I freely admit that, but maybe you can use this new appointment fiasco to get your old time back.

Tell them you would be happy to switch times to your old time slot....

Also, be sure that you don't take "no" for an answer from someone who really can't give you that "no".

Who is the boss there? The therapist or the receptionist.....