Alliance: please, get real. The more people there are in either faction, whining and moaning about how hopeless things are, the more likely that faction will lose. The whiners are spending all their time typing out their useless babble, not leading, fighting or healing. To boot, they're also demoralizing the whole group, breaking down all sense of coordination, cooperation, and confidence. If you encounter such a moaner/whiner, do not engage in any long discussion with them -- just put them in their place, "/ignore" them, and encourage others to do the same. They whiners are dead set on depressing themselves and anyone who will listen and no matter how witty your comebacks may be, and the more energy is wasted on them, the less is going into the game.
If it is in fact true that the Horde wins battlegrounds more often, then this is itself the reason. The "For the Horde" mentality bolsters the idea that the Horde is good at PvP. If you think your side is more naturally good at something, you're much less likely to think "Blizzard hates us!" when you lose, and much more likely to try and improve on your game for the benefit of your faction. Yes, there are plenty of Horde-side players who moan and whine too, but these don't fit in with the "For the Horde" spirit of the group as a whole -- and everyone knows it.