Animation Source Forums

Snowy owls, swans, chickens XD, ducks XDDD
What else...
Eagles? Can't remember the rest. Ooh, but falcons are nice.

No, the "pigeon" stands for peace. The eagle first stood for the Roman Republic, then for the Roman Empire and was subsequently used as a symbol for various empires (Napoleon's empire, Prussia and the German Reich's to name a few). It's an imperial symbol - not so free. The eagle is also a symbol for the US, but only in the US. As such, it is seen as a symbol of freedom by some US citizens, but that usage is recent and limited to the US.
Freedom/liberty is usually portrayed as a human woman, actually - see "Statue of Liberty" and "La Liberté guidant le peuple".

Well, the eagle is the U.S.'s national bird, and we consider it a symbol of freedom. White pigeons, a.k.a. doves, are traditionally a peace symbol (the whole olive branch thing), but could also stand for freedom I suppose. Most birds are pretty free.

Edit: Oh, never mind, someone else already explained that--and in better detail, too.
I might add, though, that the national bird of America COULD have been the turkey, if Benjamin Franklin had had his way!