She also asked Neville if his grandmother was well after her attention was drawn to him when he almost toppled off his pouffle (or what ever her chairs were) in the first class. When he said he thought his grandma was well, her reply was that he should not be too sure. So, maybe she could 'see' that he had a grandmother (or maybe she was just lucky in saying it because, after all, everyone has or had a grandma), but nothing happened to the grandma that we are told about, so did she really say anything that showed she 'saw'?
It was prob. a 50-50 shot on Trelawney's part. What if Neville didn't have a Grandma? We'd have automatically figured she was a clueless nutter and would've ignored her further rantings, right!? Lucky guess? Maybe! But, I think we needed those predictions to "come true" so we wouldn't think the lady a total whacko. She had to have some credibility esp. if JKR wanted us to buy the prophecy.
I do think the teacup part was put in purposely, but more to highlight Neville than to highlight Trelawney. Neville was already known as kind of a clumsy, not very good wizard and had been in her class for a while by that time. I don't think it took much foreseeing to tell he might break his cup just from observing him for a few seconds (much less half a semester). Did he break the teacup because she foretold it? Or did he break a teacup because she made him nervous about breaking one?
The breaking of the teacup happened on the first day of Divination ... not after Neville was in her class awhile. Now, remember that Trelawney didn't mix with the staff and rarely left her room so I doubt she'd have tremendous knowledge about new students as she didn't mingle w/the faculty.
As for Neville falling off the chair, I interpreted it more b/c he was caught by surprise. In the book it reads:
Professor Trelawney went on, her enormous, gleaming eyes moving from face to nervous face. "It is a Gift granted to few. You, boy," she said suddenly to Neville, who almost toppled off of his pouf. "Is your grandmother well?"
Sounds to me like Neville fell out of his chair b/c she surprised him. We're told that all the students in the class are nervous to begin with. And, if you're nervous and the teacher surprises you with a "You, boy," I'm sure you'd prob. jump out of your seat as well! Esp. if you're not expecting to be called on right in the middle of her speech.
Is she right in forseeing the things in the HBP because she's foreseeing them or because she's always foretelling bad things to happen?
Since she's always seeing Grims and ominous things, it's hard to know when she's seeing them because they are really there or when they are just illussions.
I don't know ... she called Hermione leaving the class as well as a few other things. They very well could've been lucky guesses over her own visions, I'll give you that. However, the prediction about the lightening in the tower, etc. from HBP, she was reading the cards ... the cards were telling her what would happen -- not her own "visions". Same w/the Grim ... it wasn't her vision ... it was how she read the leaves. I am sure you could argue that she misinterpreted everything, though.
I guess I'll be Hermione and leave the class. You can stay in Divinations. I'll still be friends. I'll just be dropping that class.
I'm not a fan of Divination myself so I won't be staying in Trelawney's class either. Telling the future is something that I, personally, don't buy into. See you in potions class and, of course we'll still be friends!!!!
ETA -- I'm sure that, like any "seer", she's got a 50-50 chance of getting some things right.