http://finalfantasy.wikia.com/wiki/D..._Fantasy_II%29
The first dragoon was a knight by the name of Haan, who visited Deist, the island home of the Wyverns. During his time on the island, he formed a bond with the wyverns over a thirty-year period, the first of what would eventually be many to do so.
Also:
Fighting along side dragonkin are indeed in FF lore just as fighting against them are. So you can't oppose a wyvern pet because it's not in FF lore, you oppose it because you personally don't want one, which is fine.