"The small bird flies there to the Hungarian woman, the big white one to the English."
Translation:A kicsi madár a magyar nőhöz repül oda, a nagy fehér az angolhoz.
I think because what you are contrasting is the destinations -- to the Hungarian woman versus to the English (one).
Since you are emphasising those, they would tend to go in front of the verb (the main position of emphasis). And then the preverb has to come after it because something else (the emphasised bit) wants to be even closer to the verb stem.