I often have trouble understanding psychodynamic therapy and what the rules are. Personally I can't see why it matters what day you have appointments on. I generally have appointments on about the same day, but it isn't always weekly and it isn't always consistent. I think that there is definitely a point for me when there is "too much" therapy. I run out of stuff to say if I'm not in crisis or acutely distressed about something. Then I know it's time to back off on the number of sessions I have. When I'm very stressed and am doing things like calling crisis lines or emailing my therapist at 2 in the morning, then I know that it's time to increase them.

I'll be really honest, I bet that your therapist's scheduling fussiness has a lot more to do with his own personality than anything empirically based. But if I otherwise liked him, I'd put up with it, I wouldn't count on him being flexible with the second appointment sometimes and not others though. Sounds like that might stress him out.

I am curious about the two week cancelation policy: what if you have the stomach flu or bubonic plague or something? Does he still want you to show up?