As a customer, you’re entitled to be a little bit demanding. We live in a society where “the customer is always right”. Plus as a provider I don’t want you to feel like I’m boxing you in. Your appointment should happen at a time that is most convenient *for you*. The provider is getting paid, part of the business means being “on call” to some extent.
I think you mentioned earlier you try to provide options or at least a ballpark idea of availability… which helps a lot. As a provider sometimes it feels like I have to tweeze out what the client wants and when they want it, while others are extremely effective at communicating their desires, needs, expectations, availability, etc.