On a personal level, I think that Trixie had a pretty serious inferiority complex (I've got about three pages worth of writing on this for a fic I never did, but I'll give you the readers digest version here).
First of all, from her performance she almost seemed like she
wanted hecklers. If we assume that Rarity isn't being a sort of jerk here, and that pony culture looks down on immodesty (which it seems to, at least a bit), it seems like pumping oneself up like that is asking for trouble. She wanted the chance to prove herself
against other ponies. That's her idea of a show.
Secondly, As many people have pointed out, she didn't truly beat RD, AJ and Rarity, she just made them look bad. Now, as someone who was picked on for a while, I can tell you it's easy for a victim of abuse to see 'strength' as being defined by your ability to hurt others. Now, consider the equivalent in terms of magic - if a 'strong' wizard were to repeatedly use their magic to humiliate Trixie, she could easily come to equate skill with the ability to humiliate someone.
On the whole it seems likely that Trixie was at one point the bottom half of a rivalry - with a very, very nasty rival. She feels the need to prove herself, be it to herself or just to anyone who's watching, that she is skilled - an a performer is a good venue for that. Given how she reacts to adulation(quite negatively, off the stage) she's probably looking for acceptance from another skilled unicorn.
Okay, so yeah, it's probably a biiiiiiig stretch, but the signs are all there. It's interesting to think about, at the very least.
edited 12th Jul '11 10:04:04 PM by kegisak