How to unlock language school?

You have to talk to Moro down at the Language school during the evening of Day 2. The mission should be called The Lecturer Arrives (Or the Language School Opens, if it's already open.)

You basically just have to tell the lecturer to follow you, usually if he takes a hit he'll run off down the path to the town by himself, but he stops along the way if he does that, so just tell him to follow you again if he stops and lead him to town.