Edea passed her powers onto Rinoa without her knowing and that’s why.
I don't think that explanation really works. As I'm pretty sure the 'without her knowing' bit is because Ulty is the one that passed Edea's powers onto Rinoa. Though to be fair we don't really have a whole lot of info on how sorceress powers are passed on.
As far as "why Rinoa?"....Why not?
Does there need to be some particular reason? Being on the verge of defeat she may have assumed Edea was going to be killed, so she needed to pass on her powers to someone else so that she'd have another sorceress to possess, in which case Rinoa just happened to be there.
We can also play self-fulfilling prophecy angle. Ulty being from the future means that she may well be fully aware of how the events of the game (pre-time compression) play out. Meaning that she is well aware of the parade assassination attempt before it happens, is aware that the missile attack will fail (think about it, did she really want B-Garden destroyed? Ellone was there during the attack), is aware that Edea is defeated during the Garden/Garden battle, and aware that Rinoa (or perhaps just 'a girl') would be taken to Esthar where she would be used to awaken Adel. In other words, Ulty knows how history plays out and she is simply "playing her part" in that history to try to achieve her goal (ie Sir Bahamut's Unjust Persecution theory from his Time/Ultimecia Plot FAQ). She wouldn't necessarily know the outcome of Time Compression, since it manipulates time itself.
http://www.geekologie.com/2008/08/25/ninja.jpg Everytime you see him, the phiefer's just so hype. He's dope on the board and he's magic on the mic. ~fidormula