I'm too old to bother with political correctness. Just maybe the words "feather" and "brain" have something to do with the epithet - whether justified or not.
They get in a flap, they have bird brains, they have an appetite of a sparrow, they have eagle eyes, some have thier own nest eggs, some have sparrow legs, they have varnished talons, they have eyes & ears of a hawk, they feather thir own nest.
As long ago as the 1200s, 'burd(e)' meant a maiden. That was associated with 'bryd', from which we get 'bride'. So, the connection between birds and girls/women is truly ancient.