Just to be clear, you would also need to complete the class quests for both the classes in order to unlock the job you desire. if its not letting you unlock it then its most likely that you didn't finish the class quest for the ones you need to level up to lvl15.

https://ffxiv.gamerescape.com/wiki/Categoryisciplines

I use that to follow what i need to do to unlock stuff and following the quests i should do.