Thancred listed as wrong job ?

[Enkidoh]

He is actually a bard insomuch as he wanders around quoting poetry and singing songs and swooning the ladies and has been referred to as such even way back in FFXIV version 1.0... but he is not the combat ARC based BRD Job the player has access to. Gameplay-wise Thancred starts out as a GLA before gaining ROG and NIN skills.

So it's not a mistake, it's a little quirk of the storyline that you need a little willing suspension of disbelief for (the reason why they didn't just make him the actual BRD Job in the first place is because Thancred is a character who was first introduced in FFXIV 1.0 where the BRD Job did not originally exist but was planned to be eventually added in a totally different way to how it was implemented late in 1.0's life, thus making Thancred an anomaly).

Also you need to remember that the description for the BRD Job on the Lodestone actually states there are two versions of it, the tavern dwelling entertainer, and the ARCs who started singing songs in the middle of battle to inspire morale in their fellow soldiers:

The word "bard" ordinarily puts folk in mind of those itinerant minstrels, fair of voice and nimble of finger, who earn their coin performing in taverns and the halls of great lords. Few know, however, that bards in fact trace their origins back to the bowmen of eld, who sang in the heat of battle to fortify the spirits of their companions.

From this alone, it's easy to see then that Thancred is the former, the player's Job is the later. Simple really.