Rescheduling looks like moving a box in a calendar. Behind that box there may be a day off booked months ago, a lift arranged with a neighbor, a carer paid for the afternoon. The person moving the appointment sees none of this, and the person receiving the call has to rebuild the whole structure.

Say so as early as you possibly can when you have to move something, and offer more than one alternative. Ask whether the change causes a problem, and mean the question. And when you are on the other side, it is reasonable to say what the change actually costs you rather than quietly absorbing it.