Lol!
Also, to add onto LadyKiki's response, the wyvern's priority for Healing/Remove Breath is determined by your current party list. The Dragoon is always on the top of thier list (as are all players when viewing thier own PT list), and therefore the wyvern goes by that list to determine who gets first priority for any beneficial breaths, starting from the top down.
Also, the beneficial breaths effect radius can be exceeded by players being out of range, and the wyvern will *not* move on to the next person in the list, so be very careful about how far hurt people stray from your wyvern. If someone is in deep red and remains outside of range, your wyvern will continue to try to heal that party member, and will continue to fail to do so, ignoring all others below them on the list until they no longer meet the prerequisites for aid.