For those that haven't caught up, List of confirmed flying mounts in 3.1

[Enkidoh]

I hate to burst anyone's rage bubble, but Fenrir really ought to be able to fly? He comes from Norse mythology, and he's not just any wolf, but the son of the giant Loki, who eats the moon at Ragnarok. He has to be able to fly in order to get to the moon.

Except the mount description clearly states the mount is not the real Fenrir, but just an ordinary wolf of a species called 'hoarhounds' that formerly occuppied Coerthas only to disappear when Ishgard was founded, but due to climate change have returned. They are a species, not a a single entity:

Following the rise of Ishgard, hoarhounds all but disappeared from the Coerthas highlands. However, the shift in climate caused by the Calamity has seen the legendary beasts descend from their mountain dens once more.

The item description for the actual Fenrir Horn also states that the particular specimen that is the mount was captured, broken in to be ridden on, and given the name of 'a famous Alpha male of a Coerthan wolf pack' (i.e. the last boss of Snowcloak), possibly to help make it more attractive to 'customers' at the Gold Saucer:

A gilded horn that when blown, summons a purebred Abalathian hoarhound mount named after its pack's legendary leader.

Either way, the Fenrir mount is not the Norse Fenrir, nor is it the traditional FF summon. It's... just a plain ordinary wolf. So again, coming back to the point of this arguement, asking the Fenrir mount to fly would be a conceptual nightmare. It just would not make sense.