As an illusionist, she doesn't have the ability to summon or create a familiar of her own. Her only option is to convince a supernatural creature to let her bind it instead. Since having a powerful Other at her beck and call would guarantee her a place in a coven after she graduates—and legendary treasure hoards are an added bonus—she thinks binding a dragon as her familiar will solve all her problems...
Because sometimes a girl needs a dragon, not a knight.