"i dont trust him"
how many fucking time he need to save you for you to trust him weak ass hero complex dude
Nagumo himself wouldn't trust Nagumo, if he was some other person. It's perfectly reasonable. Sure, Nagumo might be looking after his own, after a fashion (he won't pamper them), but all in all he's already inscrutable for the rest of the class, plus most of the locals. He's an outlier who does incomprehensible things they can't predict. They also sacrificed him, more or less, so while you might foremost say Nagumo shouldn't trust them, it does go both ways. If your faction betrayed someone (even if not you personally), would you expect good things from that person, if he returned alive? Perhaps that's mostly ancient history now, but it did split them forever.
Not that I'd consider Kouki an outstanding fellow, don't misunderstand me.