I dunno where people come up with the whole "Dragoon is a Anti-Dragoon class so having a pet goes against this" I have played every FF under the sun except 12 because my ps2 exploded prior to its release. I never recalled any dragoons actually hunting and slaying all Dragons.

Hell even in lore Dragoons were spiritually attuned with Dragons and fought alongside wyverns. They never had them in the actual games (until XI which was horribly implemented) but it is written in the lore this way. While it is true that they do have an advantage should they come accross Dragon opposition being that they know exactly how a Dragon ticks having worked alongside their kind using them as mounts and allies in battle.

Not all Dragons are good and those are the only Dragons a Dragoon would actively hunt down and slay.