How ridiculous on lots of levels.
Of course the school will have made this info available sooner than 24 hours before. No doubt the OP will claim that because she had not looked in the places where the info is available, the school didn't provide the info.
Of course the right approach is never to demand something or to insist that a 'no' answer cannot be given.
The best way to a bad relationship with the school and to promote poor behaviour to your child is to behave as the OP is suggesting - being aggressive, rude and demanding....and always assuming you are right.
I expect the school said 'oh well' because the info has been available for a while. Often slots are 'sign up' slots and if you don't sign up, you get what's left. TBH in this situation to then say it's inconvenient and ask for another slot is actually quite rude. To say with such short notice is quite rude - the teacher will have spent the evening after a full day at work talking to parents, the slots se allocated for that and we are all sure that notice has been given, so really parents should in most circumstances try to make their slot - sometimes it might not be 100% convenient, but hey ho, that's just life isn't it sometimes.
Is it more acceptable to inconvenience the teacher with less than 24 hours notice or to suck up the inconvenience of a slot yourself, when in reality you have failed to get to grips with what is going on? Actually, most reasonable people at this point, even with a child normally in bed by 7 would have the good grace to recognise they have messed up in not knowing what is going on and just get on with what they have been accepted rather than wanting alternatives.
I'm a bit surprised more people haven't just said, in the circumstances, get on with it and take the appointment you've been given.
Unfortunately, I know a couple of parents who never sign up for parents evenings. They don't like the days of the week they happen on or the bother of going and signing up or finding they don't get the slot they want. So as a matter of course they always just say they can't go and say when they would like to come instead. I think it's pretty rude and dismissive of the teachers time to do this.....but I think a lot of people don't think twice about asking (politely I acknowledge, not rudely as the Op suggests) for something to convenience themselves rather than thinking about the inconvenience to someone else which follows.