Most other people here have covered the basic reasons why one feels loyalty. But in PS, you knew some of your enemies as well as your friends, in a sense.
I was primarily a sniper and air cavalry. I recognized other snipers, knew them well. Knew their strengths and weaknesses. Knew some of their loadouts, we'd exchanged fire so many times, and in some cases I'd even peeked into the backpacks sitting atop their corpses.
I knew other pilots, which I could engage one-on-one, and those that I needed to call for support on. I had a strong respect for some of my rivals, despite my disdain for the rest of their empire.
You knew some of the enemy commanders and outfit leaders too, and seeing one on the battlefield surrounded by his platoon was a moment of excitement for a sniper or a pilot. Sometimes you'd be flying sorties over a hostile enemy base, strafing armor and infantry, when suddenly an enemy air cavalry outfit shows up and an intense furball develops. You'd know who they were, skilled rivals that left you calling targets over comms, working hard to avoid getting shot down while answering the yells for assistance of your squadmates who couldn't shake someone off their tail.
That's why an MMOFPS like PS is so awesome... match-based FPS completely miss a critical element; pride in your faction, and rivalry with your most dangerous enemies.