so this is what death is all about
The Timber mission is, to put it mildly, a clusterfuck. The train job goes to hell, the president is actually a zombie, and the first time in 17 years anybody manages to put on a TV broadcast it ends up with Seifer stealing the show and ruining the picture quality. What the hell, man.
Having acted on his own to take on the president of Galbadia, Seifer likely faces dire consequences — ones that Squall doesn't hesitate to acknowledge when the others ask him about it.
Quistis: What's going to happen to Seifer?
Squall: He may already be dead.
Rinoa: How can you be so casual? I feel...sorry for him.
Squall: (...Feel sorry? Seifer would hate to hear that.)
Rinoa: What's so funny!? You're terrible! So...why do you think Seifer may already be dead?
Squall: (Because...) The president of Galbadia and the sorceress joined forces. Seifer attacked the president. It's no surprise that Seifer may have been killed because of it.
Rinoa: Even so! I still hope he's alive.
Squall: (Think what you want. ...Reality isn't so kind. Everything doesn't work out the way you want it to. That's why...) As long as you don't get your hopes up, you can take anything... You feel less pain. Anyway, whatever wish you have is none of my business.
Rinoa:...You're mean. MEANY!!!
Squall: (What's with her...?) ...Sorry.
Squall's reaction here is more about his own personal mindset than anything else, as indicated by his internal monologue. He's so much of a pessimist that he's perpetually steeled himself against negative outcomes, refusing to hope that anything will actually go well. It's easier to deal with shit going bad if you never let yourself think it'll go right in the first place.
Furthermore, as a SeeD, dying on a mission — even a self-appointed one — is perfectly normal. There are consequences for the things they do, and he's prepared for them. Squall's answers are clinical, textbook. Having spent most of his life at Garden, he doesn't get why Rinoa doesn't see this, and can only offer her a dismissive apology at her reaction.
Anyway, one train ride, whacked-out dream sequence (sup Laguna), and journey through the forests later, the party ends up in Galbadia Garden. And that's where they find out Seifer has been executed.
Each character has their own reaction to the news, and Squall has to talk to all them before we see his. There's a pretty common theme running through them — aside from Rinoa, who was much closer to him, the SeeDs are all fairly detached from the loss. Considering everything we've seen from Squall, you'd think he'd be quick to box it all up and put it away. Not this time.
I didn’t cap it, but right after this, Squall has the strongest emotional reaction we’ve seen from him in the entire game. He completely rejects this idea, that he can just die and that’ll be that, people will talk about him and decide what kind of person he was.
Squall doesn’t emote. Let me repeat that: he doesn’t show emotion. Ever. Squall is one cold motherfucker, but not only does he exclaim here, he runs out of the room, unable to deal with it. It’s not the news that gets him, mind. We see how he reacts to Rinoa, to Quistis, to Zell. Squall has his own private reaction to the news. It’s when he thinks about it in terms of himself — because, ultimately, Squall thinks about everything in relation to himself first, he’s too self-absorbed not to — that he freaks out.
He can’t die. Not as he the person he is here and now. He’s not satisfied with himself — he may not admit it, but he sure as fuck isn’t happy — and everything he’s learning on this journey is telling him that there’s a lot more he needs to do in his life. And that terrifies him.
See, no matter what he said back in Timber, Squall can't just put everything in a tidy little box and forget about it. This is a guy who's so shut off from his emotions that it takes a disc and a half just for him to trust in the people closest to him. And the thing about emotions is that when you try to bottle them all up, eventually they're going to come out. No matter what Squall likes to think, he can't just pretend his own feelings don't exist.
Is it any wonder he freaks out and runs out of the room? The guy hasn't shown any actual emotion in the entire game. He's not a sociopath, he's just a kid with a screwed-up childhood who has no idea how to open himself up. I'd worry a hell a lot more if he didn't have a moment where the mask broke and he lost his shit.
The other important thing in this scene is that I don't think it really occured to Squall until this moment that he could actually die. It doesn't matter what kind of training he has as a SeeD or how pessimistic he is: he's 17 and he thinks he's immortal. He doesn't really think he's going to get himself killed. But here he is finding out that his rival, who he says "wasn't really a bad guy, he was one of us," is dead. Squall's been a SeeD for a matter of days, and reality is setting in.
I'd feel remiss if I didn't bring up the Squall's Dead theory here, especially as we reach the end of Disc One. Even if it’s not how the game’s meant to be read (I go either way myself, I think it’s a fascinating take on the story but not necessarily how the game was intended to be understood), Squall is about to have a very close brush with death himself. Of course, it's one that's never mentioned again, but that's FFVIII for you.