I cried about this fic all over again while trying to find this conversation 😭😭😭
Awww <3 It was a fun challenge to write, so I'm happy to hear it still has such an impact on you!
This argument between Noctis and Gladio really comes down to who is at fault and how much they are at fault for Noct's brush with death. Noctis, obviously, thinks it's his fault for not having the elixirs, flasks, etc. that would have allowed him to replenish his magic and made him able to finish the fight with less of a struggle. He also carries a HUGE amount of guilt for not carrying any phoenix downs on him--Prompto absolutely could have been permanently dead if it weren't for some stranger who did make sure she kept her allotted stock of magical supplies in order at all times.
Noctis sees this whole event as a failure of his own personal responsibility. Gladio and Ignis and plenty of others have gotten on his case before about Doing Things--and he doesn't always do them. And because of that, Prompto almost died. Other people did die. What if he'd had a phoenix down in the armiger as he should have? Could Valeria's then have been used on someone else? Could they have revived two people instead of just Prompto?
He won't ever know because he fucked up by not doing the simplest thing: being stocked up on healing items.
For Gladio, this whole event is a failure of duty. He should have made sure Noctis has all of the curatives he's supposed to at all times instead of just trusting Noctis to do that. He should have done a better job of training Noctis so that he could better fight against groups of people. The Crownsguard shouldn't have ever farmed out part of their security duties to other entities, no matter how much Noctis wanted a "normal life."
All of that, plus he saw Noctis almost die. There was absolutely nothing he could have done because Noctis was without trained support and Gladio was too far away to be of any use at all. This isn't some drunk being belligerent--Noctis nearly died. His friend, his brother, his charge he's pledged to die before. It is very safe to say that this whole thing just scared the shit out of Gladio, and he's furious with himself for everything that happened and for being scared.
Plus, Gladio just got a very ugly front row seat to his own decision making process, which meant deliberately deciding that Prompto should be put in harm's way for the smallest chance of buying Noctis time. And that temporarily cost Prompto his life. (And he's also furious at himself for that one moment of hesitation, in which Cor beat him to asking Prompto to help. He should have made the decision immediately and dealt with the horror of it later.)
So Noctis thinks he's at fault and wants Gladio to agree with him because getting reamed out by Gladio will momentarily satiate his budding survivor's guilt. Meanwhile, Gladio has fucked up on several more levels and definitely believes he deserves whatever criticism and fury results from this event. These two tend to butt heads disastrously in canon, and they both kind of--just seek each other out for a mutually self-destructive moment.