The whole charm with Mazzy is that she knows she cant be a paladin, but she still behaves like one. That makes her, in my book atleast, far more interesting than any regular goody-two-shoes. Starting her out as a paladin just makes her another mass-produced righteous crusader against blah blah blah. Although it would make for some interesting dialogue.. Mazzy: "I wish I was a paladin..." PC: "Uhhh.. you are a paladin." Mazzy: "No, Im afraid that's just not possible." PC: "But you're wielding a holy avenger and all!" Mazzy: "Im afraid as a halfling, I cant be a paladin. Maybe some day..." PC: "And I thought Minsc was bad."
As for in character reasons for Mazzy to be a fighter, not a paladin, here's a few:
Being a paladin requires more than good will. Its more than just being a really nice fellow with a sword, its about being a chosen warrior of your god. Because Avoreens church hasn't had any paladins(or they are so rare to be mostly unknown), there are no strictures to follow or trials to undergo in order to prove herself a paladin.
Lack of faith. While Mazzy seems quite devout to her godess, she doesn't have all that much faith in herself. If she's convinced that she cant be a paladin, she doesn't have the faith for it.
Avoreen doesn't support paladins. While she's a good goddess of war, she's also the halfling godess of war. Halflings are not a physically strong race, and so open combat is not something that should be encouraged. Avoreen might support rangers instead of paladins, leaving Mazzy pretty much out of luck.
The grand destiny. Mazzy will eventually become a paladin, but since she's the chosen one/the first halfling paladin/so darn cute/whatever, she must first learn humility and patience.