I don't think that's it....
My theory (mind you, it's a mock theory), which I haven't posted anywhere except DeviantArt, is that Xion is a replica of sorts of Namine or Kairi, whichever you'd like to look at it, who is able to wield the Keyblade, something that Namine is not able to do. Xemnas had her created because he started getting impatient with the whole defeat Heartless = Creation of Kingdom Hearts, so he wanted two Keyblade masters in his Organization instead of one.
Xion was created and became best friends with Roxas due to them being around the same age and the fact that they both wielded Keyblades. Through Roxas, she met Axel and vice-versa.
One day, Xion learns of Namine and how she is Kairi's Nobody and thus begins to wonder. Wasn't she, Xion, also Kairi's Nobody? How could this be? How could a person have two Nobodies? And thus, she seeks Namine out. The two converse (as seen in the trailer) and Xion learns of her being a Replica or something and not really a Nobody, or anything really.
This is too shocking for her, so she runs away. Xemnas doesn't want to lose her, so he sends Axel after her. They have their little fight and in the end, despite whatever the outcome would have been, Xemnas decides that Xion really isn't worth all the trouble and has her eliminated. =) Leaving Roxas as the only Keyblade wielding member of the Org.
This is a mock theory, I'm not really being serious with this. Feel free to express your opinions about it. =D