There is no "One", either

When I saw The Matrix for myself, I couldn't help but notice, as things progressed, that being "the One" seemed to not be an inherent thing at all, as Morpheus, Trinity, and most of the rest seemed to assume, but a state of mind. With that in mind, two revelations about what the Oracle said to Neo came to me:

1. When she claimed that Neo was not "the One", what she said was true -- at the time. Note that she said next that he seemed to be waiting for something.
2. The part in which Neo broke the Oracle's vase after she apologized for it ahead of time ended with a suggestion on her part that he might not have done it if she hadn't said it would -- a reference to the concept of a self-fulfilling prophecy. Did she merely say that "the One" would be "reborn" because she knew that the resistance needed someone who could reach the state of mind necessary to exercise control over the Matrix?

Actually, I have to dispute this and say that I do believe that there is such a thing as The One. Remember the saying that reminds you, no matter how good you are at something, there's always someone who can do it better? Keeping that in mind, who's at the top? Who knows more than everyone else? Someone who is so masterful at what they do, that they are the one who leads everyone else? Neo is this person, and he leads. He, like so many of us geeks strive to be, has the ultimate understanding of everything around him. He is able to bend it to his will, and is a master at this. "There is no spoon" is his mantra, and it is what he teaches to everyone else.

While we're on the topic of Neo, study his name for a second. Neo? Hello, that means such things as 'new' and 'reborn'. The very moment that he selected his name, he was affirming his legacy. This should speak for itself in terms of the importance of online aliases or nicks, which I know some of us have difficulty understanding.

By the way, don't forget that "Neo" is also an anagram for "One"

Don't you ever have that feeling that the path you select at any given time is right, without knowing all the facts? Some would call this intuition, and I believe heavily in following one's intuition, their natural instinct of right and wrong. Nicknames, especially mine, should be an instinctual decision, and I (for one) am proud of it and what it represents to me! Thus, Neo was also proud of his legacy, and simply followed his intuition. It takes an extraordinary, intelligent, and highly aware person to do the right things based on their intuition.

Such is the heart of what The Matrix was all about. Finally, I must counter your points as given above:

1. She did not claim that Neo was not The One. She merely said "Sorry kid" after Neo said "I'm not the one". Listen to the quotation in question again. The tone of her voice is such that makes it sound like she's sorry and dissapointed that he doesn't believe in himself just yet. Her frustrated attitude right after the quotation also affirms this. That quotation, I'm sure, was purposely planted in the movie to throw people off. The reality is that The Oracle probably heavily believed in Neo being The One, but was upset in the fact that he hadn't come to this realization.
2. The Oracle didn't apologize for it ahead of time, Neo did afterwards. You're also forgetting one other thing here; what if Neo hadn't been made aware of knocking over the vase? Why do you think she mentioned that it'd probably "bake his noodle"? The vase is not a self-fulfilling prophecy because if he was not made aware of the vase, Neo would not have turned and knocked it in the first place. Nobody would've.

Neo is The One.

When the Oracle talked with Neo, she said he wasn't the one YET, that he was waiting for something; "Maybe your next life, who knows". And Neo doesn't really become the one until his next life (after he dies).

Also, Neo isn't the first one. It seems to me that there are links between being the One, and being the Buddha (note that the kid who tells him "there is no spoon" is often call the Buddha Child). Both the One and the Buddha are defined by a state of mind, realizing the truth about the world.