It's probably most accurately interpreted as both sides having their heads so far up their ass that they're escalating at every step:
-Asarnil walks off with part of the army to pick his own fight and wins the fight.
--He's actually not at all in the wrong here, in a medieval equivalent army, the field leader is given a great deal of independent authority, including the authority to take said army to engage an enemy on his own initiative like Kazador could have done if we just kept him waiting too long. Like we could have peeled off the wizards of Eight Peaks to do whatever we wanted when we got assigned as their warleader.
-Asarnil expects to be given a parade(or equivalent) in honor of his victory.
--This is reasonable...taken in a vacuum consisting ONLY of the battle and the victory.
--Its like if Mathilde took the Undumgi from their Caldera post during the Battle of Karagril and went to assault Moulder on her own initiative, winning, but if Belegar needed a pike unit in the Caldera at the time...whoops?
-Finubar tells Asarnil to meet him, possibly to get an after action report explaining what the heck.
--This is reasonable by the standards of anyone except maybe drama queens.
-Asarnil is outraged by the idea of needing to answer questions instead of being immediately honored as the hero of the day. He flies off in a snit, making a big show of it.
--This is unreasonable by any standard. Your King calls you for an audience, you don't refuse him like that.
-Finubar, as a sovereign, cannot take being disrespected like that without damaging his authority(if Asarnil had just stomped off maybe, but flying off on a dragon is not subtle and certainly the gossip item of the year). He doubles down and tells Asarnil to show up or lose his citizenship.
--While probably not the best plan, such a demand is well within his authority. And however much I like Asarnil, Finubar certainly considers his authority being more important than the feelings of one hero unit.
-Asarnil doubles down and loses his citizenship, pending a public apology.
--This works out fine for Finubar, he has more dragonriders, even if Asarnil is a really good one, and heck, even in exile Asarnil is furthering his foreign policy, by showing how badass elves are, by fighting gribblies in the Old World without stepping on human toes by deploying foreign militaries on sovereign soil, and by keeping one loud and clearly unable to control himself Caladorian prince out of his court.
Now, this all worked out in our favor, Asarnil could have been any random Proud Caladorian Prince back home continuing to push for isolationism or gloryhounding.
Instead, he's applying dragon to solve problems, at the expense of merely money.