http://dictionary.cambridge.org/define.asp?key=31790&dict=CALD
make the fur fly (ALSO set the fur flying)
to cause a bad argument:
He set the fur flying by demanding to see proof.

http://dictionary.reference.com/browse/fur
make the fur fly
a. to cause a scene or disturbance, esp. of a violent nature; make trouble:
When the kids got mad they really made the fur fly.