Such an interesting clash of cultures. Are you Gen Z by any chance OP? You seem to need your manager to demonstrate that they value your time, because to you they are asking a favour, in a way, by asking to meet with you. They are asking for your time, when you'd maybe already planned to prioritise it another way and asking you to do something different, which doesn't respect your autonomy in your work, and gives you an additional task to do.
That feels more like Gen Z than older middle management Millenials or Gen X bosses.
I think there are some places where line managers need to signal that they have a keen interest in their managee's development. I would always do a set-piece approach to booking monthly 121s for instance and do loads of the admin myself as a boss. This shows I take supporting the team to develop seriously. I wouldn't say "Just find a time in my diary and pop in your annual appraisal". That doesn't give it the right gravitas. And I do value their time and development and want them to have a good and productive meeting with me where we can both share feedback. It's on me to make that space work.
However for a project meeting or a quick catch up about emerging developments I would expect to be able to say, effectively, I need you to reprioritise your time to give me some more of your time, please find a slot. I find it a bit laughable and naive (Sorry, I am Gen x!!) that someone needs this level of stroking and validation about the value of their contribution that they would need the booking politely done for them. It isn't actually a request, it's an instruction to have that meeting. Truth is you're less experienced than your manager, literally of less value to the organisation financially; so time bound admin tasks need to be considered with that in mind. Your contribution is valued but you also should be (sort of) grateful for the opportunity to report in, hear about the business and learn something from your manager. They arent meeting you because they are somehow getting a personal kick out of throwing their weight around, but because they need to know something about your work, maybe course correct you, or identify an upcoming issue, or let you know something strategic that will affect you. Rightly, you know less about what they are juggling because they have to weigh up priorities on a bigger canvas than you.
They also have to show up more prepared, calm, in a leadership mindset, and use more skills to manage themselves than you do. It is their prerogative to arrange their day such that it enables them to do this successfully. So you ultimately have a better time at work as they show up better ready to lead you.
I'm afraid I'm with the person who thinks you could just change your attitude as you seem super entitled to be honest and if I were your boss I would think about whether you were ready for more responsibility.