Good question. Maybe it’s still open to debate amongst the creators.
But as far as possible reasons go, here are the most likely:
[ol]
  [li] Mage orders send their mage in duels to the death in order to test and perfect their might and strategies in anticipation of a major conflict.[/li]
  [li] Mages are so hubris-filled (egotistical) and bored of being so powerful that training for a duel in the Mage Wars is one of the only interesting thing to do with their power (doesn’t really fit with the Priestesses or with the Wizards’ plot to stop other mages from channeling).[/li]
  [li] They are so proud they want to prove their God or order is the best of them all and are ready to die to prove this point.[/li]
  [li] They fight in the arena to avoid killing civilians pointlessly in wars. Corollary: major political disputes are settled in Mage War duels. Other corollary: Warlocks are outnumbered in any conflict and they prefer their chances of killing other mages in duels rather than in open war.[/li]
  [li] Mages are cursed or forced to fight in the Mage War by some extraordinarily powerful entity or external force.[/li]
  [li] The rewards of winning duels outweigh the risk of dying. (Unlikely... Why would Westlock give such riches or power away?)[/li]
  [li] A code of honor exists amongst mages that oblige them to accept challenges. (Kind of like Kanly in Dune)[/li]

[/ol]

My guess is: a combination of 1, 3, 4 and 7 and a little bit of 2 for some brash mages.