I was always alone
I'm still not over the fact that they go into space. Like, okay, it's one thing to find out Ellone is up on the space station, but she literally just went up there because Laguna was there for an inspection. And then Squall and company show up, and the Esthar officials are all "well sure we can send you up there too just get in this little pod." It's not like Rinoa's condition was all that life-threatening if Squall could carry her from FH. They could have just waited for Ellone to come back down. But nope. Gotta go to space.
This game, I swear. Cid Highwind would pitch a fit.
Anyway, so off they go to space
to play cards no seriously fuck the Lunar rules because heading to the one place in proximity to the worst sorceress in recent history when you're in the middle of a Sorceress War is a great idea. Seriously, I can't even begin to describe how ridiculous this entire sequence of events is. I know it's necessary for the plot, but... well, no, is it even necessary? Seifer was already getting the Lunatic Pandora moving down below, and it's not like Ultimecia couldn't have controlled Rinoa once the Lunar Cry knocked Adel to the ground.
I just. Gotta go to space. That's all there is to it.
Okay, anyway. This is actually the most important part of the game in terms of Squall and Rinoa's relationship and I'm putting off discussing it to snark about how ridiculous FFVIII is, so let's get to it. Squall, who's already done a lot to get Rinoa and Ellone together, outright begs her to send him to Rinoa's past in a desperate attempt to save her — even as they're getting in an escape pod to get off the space station before it's destroyed.
Ellone: Squall, you should be protecting Rinoa, not me. You're the only thing on her mind right now. She's calling you.
Squall: Ellone, take me to Rinoa. Please.
Piet: Next! Hurry!
Ellone: I don't know if I can send you. I don't know.
Squall: GOD!!!!!! Rinoa is gonna die! ...I can't take it. Ellone, please. I've never felt this way in my life.
Squall: Take me to Rinoa...to her past.
Ellone: Ok. It may not work, but we'll try, ok?
Piet: Come on! We have to go now!
We've seen enough of his life to know that Squall has never reacted like this before. The only thing on his mind is Rinoa, not their imminent deaths by falling debris and/or monsters. She's all alone out there in the cold emptiness of space, and he can't let her die.
How could he? She's the one who's fought so hard to save him from his own loneliness. And just as everyone around him gave up on drawing Squall out of his shell, they give up on Rinoa, too. How can there be any way to save her?
Squall doesn't care: he tries anyway, just as Rinoa tried with him. Sure, it's on a totally different scale, and it's a matter of life or death this time. But Squall never really does things halfway, and as stupid as it is to go after her without so much as a tether, there's no denying it's romantic.
Finding the Ragnarok is, of course, a deus ex machina, but we'll wave that aside for now. One of my favorite things about this whole sequence is when they get inside and Rinoa asks for a hug. Keeping in mind that Squall has literally carried her on his back across half a continent and gone out into space after her, he gives her a blank look and flat-out does not get what she wants a hug for.
It's hilarious and tragic all at once. Rinoa's used to seeking comfort, like she did after the incident in Deling, but Squall never, ever does. He's full of so many abandonment issues that comfort itself has become a foreign concept to him. And he says as much when Rinoa climbs in his lap.
Squall: Why are you holding onto me like this?
Rinoa: You don't like this, Squall?
Squall: Just not used to it.
Rinoa: How about when you were little? Didn't you feel safe and secure being held by your parents?
Squall: I can't remember anything about my parents... But...Ellone was there for me. Ellone was there to hold my hand.
Rinoa: Made you feel safe and secure?
Squall: Sure. But she left. Just disappeared. I'm afraid.. Afraid of having that feeling of comfort taken away...
Rinoa: You were afraid of losing us? Is that why you kept your distance?
Squall: I was always alone...
Rinoa: Squall... You missed out on all the good things in life. You've missed out on so much.
Rinoa: Definitely. I like it like this. I liked having my mom hold me. My dad, too, back when we got along.
Squall: I'm not your mom.
Rinoa: No, of course not. But now... Squall you're the one who gives me the most comfort. Comfort and happiness... And annoyance and disappointment, too!
Remember, of course, that this conversation takes place as the game's love theme (both in-universe and out-), "Eyes on Me," is playing. Usually when you hear the love theme, you expect the characters to be passionately declaring their feelings for each other, not documenting reasons why one of them is in dire need of extensive therapy. FFVIII is a love story, but it also very clearly demonstrates that Squall's personality is the result of his horribly warped childhood, and the lessons he learns in the games are ones that really need to be addressed by actual therapy once the saving-the-world business is through with.
Squall doesn't understand it himself; he has no way to. But Rinoa understands, and she feels for him, even as she dreads what awaits them on the surface.