Firebreathing is not just a card, it is a word associated with a common ability that has appeared on creatures over the years–Shivan Dragon being one of the first. Moonveil Dragon takes this ability and expands it: you can use red mana with its ability to raise the power of all creatures you control.
When a creature with ‘normal’ firebreathing leaves play, the increase in power does not matter as the creature is no longer around. However, as Moonveil Dragon’s ability does not just apply to itself, it is important to remember that the effect from this ability will still be applied even after it leaves play. Even if the Dragon is killed in response to the ability, the ability is already on the stack and will still resolve normally (though obviously it won’t benefit the dragon itself, it will still boost your other creatures).
For example, if the ability of Moonveil Dragon were to be activated three times, each creature controlled by the dragon’s controller, including the Moonveil Dragon itself, will get +3/+0 in total. If the Moonveil Dragon were to leave play, the other remaining creatures will continue to get +3/+0.