I have one from work yesterday. I answer phones for part of the day and many of these calls are requests to make appointments with our providers. Usually, to make things go a little faster I will ask "Is there a particular day of the week you'd like an appointment, or would you just like Provider's next available opening?"
Usually this prompts people to provide me with even more information that makes it easier and faster for me to find them an appointment. For example, many times people will respond "Oh, just the next available opening after 2 p.m." or "Any day except Tuesdays." Sometimes it doesn't, and people just respond "Oh, the next available opening, please." and then reject the first five appointments I offer them because of conflicts. This is fine too, I understand that sometimes you don't remember everything you have planned, or you don't expect me to only offer you appointments that won't work with your schedule. Eventually, we find something that works for everyone.
Yesterday I had a woman call and request to make an appointment with her provider.
To save me typing it every time, read all of her comments in the snottiest tone you can imagine.

Me: Is there a particular day you'd like to schedule for, or would you just like his next available appointment?
Her: What is his NEXT appointment, please?
Me: His next opening is on Wednesday at 10.
Her: And the NEXT one?
Me: He has an opening on Thursday at 11.
Her: [Big sigh] And after THAT?
Me: His last opening this week is on Friday at 10.
Her: Okay, well you're just inching along. WHAT does he HAVE in the next couple of WEEKS?
Me: [Lists off several available openings over the next two weeks]
Her: Look, I'm trying to make an appointment. WHAT would you SUGGEST I do?
Me:

Well, if you can tell me a day and time that will work for you, I can see if he has an opening around then.
Her: Never mind. I'm going to hang up and do this a different way.
I still have NO IDEA what I was doing wrong!