When you say that I'm feathery, that's quite clearly wrong,
If I come from the trees then you can join me in song.
I've nothing to wag, but you imply that I do,
I have nothing to sell, but you suggest that's untrue.
You say I'm unwell if I give you no prize,
If you ensnare me I'll bring tears to your eyes.
You say that I'm angry when I turn to the side,
But call me divine and you'd better all hide.
Question: Who or what am I?