YANBU.
When I broke my tooth one December, my dentist didn't offer any emergency appointments and said I'd have to wait over a week to be seen, even though I was in absolute agony and couldn't eat, or sleep due to the pain. They did prescribe antibiotics without seeing me to be fair, but they had no effect.
When the abcess caused my face to swell up like a balloon, they still couldn't find a way to treat me. Yet other practices keep appointments back for emergencies.
I called back a few times over the next few days to see if they had any cancellations and managed to bring the appointment forward by a couple of days, but the reception staff were so rude every time.
Then the receptionist called with a new cancellation, still a couple of days away and when I was trying to ask a couple of questions she kept talking over me, in a really patronising, snappy manner.
She then told me that they won't do any treatment at my appointment as it's just an assessment and they are unlikely to fit me in for any treatment before Christmas, which made me cry considering the huge amount of pain I was in.
She said in a huffy voice, "Look, if they CAN help with the pain, they WILL. Alright?!" What a lovely, sympathetic reaction!
I asked how they might do that, so I know what to expect. I was never once rude, but I was tearful, as I was in a lot of pain.
She huffed and said, "I don't know do I? I can't see into your mouth! I'm not a dentist!" Wow, nice.
To which I replied, "Any chance of dropping the attitude, stop patronising me and speaking to me like a human, instead of a piece of crap?" (She'd pushed my buttons by this point).
She replied, "I'm not taking to you like crap. I've bent over backwards for you by offering you a cancellation!" Ermm, not really. It's your job is to book appointments!
I rang every single dentist in my town and managed to get in with one. Was seen that day and he tooth removed.
Personally, I think that if they despise patients so much, maybe they should find a different job? They are dealing with people in pain, who needs empathy and help.