Okay so this is much more speculative than my other theory, but keeping that in mind…
The one scene in season 1 where Keith is mad at Pidge for wanting to leave has always struck me as somewhat odd and out of the blue…then I had a thought.
If Keith has an abandonment issue (which obviously I believe he does) that might be part of the reason he snapped at Pidge.
He may not have known Pidge for very long, but even so, he doesn’t want them to just leave. And while what he says is:
“And that means we can’t defend the universe against Zarkon.”
I don’t believe this is the only reason that Keith is mad about it.
Now, it is clear from season 2 that to Keith, his role as a paladin is really important to him. It’s even obvious in season 1. He turns his back on his past and his father in season 2 to protect the Earth (albeit in a hologram, but one he thought was real and he still made that choice)- and in season 1, he’s one of the few who immediately accepts his duties as a paladin with no hesitation. Pidge, Hunk, and Lance are all reluctant- all because of their families, but Keith isn’t.
So when Pidge says they want to leave, Keith understandably does not react well. However, it’s not just because they won’t be able to form Voltron. The next thing he says is:
Other than Shiro, the Voltron paladins, Allura, and Coran are the closest things to friends that Keith has. They’re the closest thing that Keith has to a family. And what (probably) happened to the last people Keith considered family?
His father left him, and Shiro disappeared for an entire year. And while Shiro didn’t leave him voluntarily, his father did.
While Hunk talks about wanting to see his own family, there is a very deliberate and not-so-subtle close up of Keith’s expression:
His eyebrows are furrowed- he’s angry, and it almost looks like he might be remembering something, since he’s not looking directly at anyone, just down at the ground. Then he blows up at Pidge, and actually steps forward in a confronting way.
The problem isn’t that they’re putting the lives of their family above everyone else’s, though. The problem is that they’re leaving the Voltron paladins to do it- and by extension, they’re leaving Keith.
He’s projecting the anger he has towards his father at them because they are doing (what he feels) is the exact same thing.
And this is something else that just wouldn’t make much sense if Keith’s parents had straight-up died.
It takes Shiro, the only person who has actually stood by Keith, to calm him down, but even so, Keith spends the rest of the scene staring at the floor, and moping in the background.
This makes me wonder how much about Keith’s past Shiro really knows (or how much Shiro remembers about Keith in general).
TLDR: Keith has serious abandonment issues- and that might be the reason he reacted so strongly to Pidge wanting to leave in season 1.