Ayano: Where did you even learn a phrase like that?
Catherine: From a correspondence course.
Kaze no Stigma really does have some marvelously funny moments. This in particular was brought about by Catherine's terribly odd epithet for Ayano, 巫女姫, miko-hime. The third character gets tossed around a lot in anime particularly, being full of both high status young women to whom 姫 can be applied as well as actual princesses. Of the first two characters, 巫 is the kanji for prophet, medium, fortune-teller, or in some cases for shrine maiden itself, though with the addition of the second character 女 (woman) it can only mean shrine maiden. Those unfamiliar with the tradition of shrine maidens should watch Inuyasha for a 100% realistic account of what shrine maidens do on a daily basis. Putting Princess and Shrine Maiden together nets us something like "maiden princess" in Hulu's translation, which probably contains connotations I can only guess at. But wait, there's more! Not only is this construction a bit awkward and formal, it is a subtle pun.
In Japanese, most characters have (at least) two readings, one for when the character is used as a single kanji word and one (often more than one) for when it is used in a compound word. So 女 in a compound word is read as "ko" while on its own would be read as "onna", and would still mean "woman" in either case. 巫, similarly, has three readings, "fu", "mi", which is the one used here, and "kannagi". That last one should ring some bells, and as much as Catherine uses it to mock her, Ayano literally is the Kannagi woman princess. Not that there isn't some validity to the "virgin princess" aspect to the epithet as well.
The bottom line is that between kanji with multiple readings and the fact that the same sounds can mean different words makes Japanese a magnificent language for puns.