As Kret mentioned, this was explained just prior to launch on the old Lodestone which has now been shut down - it's due to the fact they completely redesigned class and Job abilities, meaning the old abilities you learned no longer exist, and thus you have to learn new Job abilities by undertaking the Job quests.

Given the fact the DRG Job quest storyline is now also indirectly connected to Heavensward's story, there is also a story reason for undertaking the DRG Job quests in particular.