Just some comments to balance the scale a bit. I think Admiral Byrne is misunderstood and I think in R2 the reasoning for his passiveness will become more clear. Also, 1st fleet keeps the UEF in the fight just as much as 2nd or 3rd fleet. In Darkest Hour, Steele launches a huge attack on Earth. If first fleet was off playing subspace chess with Serker team or something like that there would be little to keep the UEF infrastructure intact. I believe that would be the end of the war right there. Defense is deadly!
The interesting thing about the UEF military breakdown is that they all are playing an important part in the war, even though the Admirals disagree with one another.
And about first fleet culture, you gota love the rooks. Cockpit jockeys fresh out of school with attitude to spare. Kassim for example: Ubuntu vs. War, Cooperation vs. Barbarism, Thought vs Instinct. These ideas tear the character back and forth. Kassim might come off as immature, but he's hard not to identify with at some level. It's also true that 2nd and 3rd fleets have their rooks(or had them as the case may be), but from my understanding these fleets don't appear as 'green' for some reason.
And here's why Admiral Byrne is a good guy, he's calm. Not calm as in 'this guy doesn't get it' kind of calm rather more thoughtful. That's important when you are leader of a fleet. An informed mind and a stalwart resolve. Understated and underestimated.
Just being a counterweight, this does not mean I have a bias towards first fleet or anything like that.