Save your location and talk to Kafra Milenia again. You are able to complete the quest without saving your location, but it is advisable.
"Let's assume you slipped or something during a great battle and got knocked out by a monster. You'd have to start again, wouldn't you? However, if you never saved your game prior, you'd start again in front of the dormitory. This means you'd have a lot of running to do to get back here! Pretty inconvenient, right?
So that's why you must use the Kafra Location Save Service! Just talk to a nearby Kafra employee and select [Save Location] to save your current spot. It will then let you start again from the Kafra Services site if something goes horribly wrong.
You don't necessarily have to save, but it's recommended."
"Well done! From now on, you'll start again from this very spot!
Yes, I've saved your position anyway with kind thoughts of my own, such as 'There might be someone who didn't save and will be sent back to the Elemento Academy! They might blame me for not insisting to save their location!'
No worries! I'm giving you a Butterfly Wing, which will return you to your saved location upon use. It's on the house!
Kafra Services are provided at other locations so be sure to find them!"