Justified: Mages in the Tales of Troperia either channel the power of Goddess Sophia (for White Mages) or Archfiend Centurios (for Black Mages), and the two are eternal enemies.
Combining the elements of "White" and "Black" makes for incredible power, so there are no White-only or Black-only mages.
Magic has a wide range of uses; mundane science and technology can only be used for combat or healing.
As more magician characters are introduced, we find out there are many different types of magic.
The distinction between black and white magic is political, rather than metaphysical. There's nothing stopping Marco from picking up healing magic or Claudia from learning combat spells. "Black" magic is simply any form of magic not sanctioned by The Powers That Be, who would rather ban magic in general but find that "white" magic is simply too useful to regulate.
...Which are all branches of either black or white magic.
There are two groups of The Powers That Be and each one approves/disapproves of the opposite kind of magic. The distinction is religious/spiritual rather than political.
Parodied: A bard in the Tales of Troperia writes a song titled Black or White to ridicule the situation.
Zig Zagged: Claudia learns black magic, Marco learns white magic, then both of them drop the black and white magic and use Summon Magic instead but Marco's summon magic is for calling monsters while Claudia summons supplies like food and medicine.
There are no magic users.
The branches of magic have nothing to do with black and white.
Enforced: "We could do with more than one magic user in this game, but we need variety!"
Lampshaded: "Why on earth can I heal wounds but not inflict any?" or "Why can't my magic help anyone beyond killing their enemies?"
Invoked: Claudia and Marco are novice mages, and they are forced to learn healing and offensive spells to protect and heal, respectively.
Exploited: Emperor Evulz finds a way to separate the duo, and they are at a disadvantage because Marco can't heal his wounds and Claudia has no attacks. Dennis, Hiro, and River are then unable to defend themselves because they can't use any magic at all.
Marco: "Well, of course I have a few healing spells! What kind of self-respecting wizard limits himself to throwing fireballs all day?"
Claudia: "Naturally I studied offensive spells in addition to healing. Any place the later is needed is guaranteed to be dangerous."
Conversed: "Man, I don't know who to pick, that cute chick in white or that sexy magician dude in black."
Deconstructed: Black mages are seen as pariahs for having powers that are solely destructive in nature, and are forced into either military service or exile. White mages, on the other hand, would be seldom seen outside of cities and other major population centers, since their services would be in such high demand for everything from common illness to life-threatening injuries.
Played For Drama: Marco joins the hero's party to prove that Black Magic can be used for good purposes, while Claudia joins up because she's sick of her responsibilities and wants to see the world outside the city walls.