Frighteningly enough, this behavior is also present in real chickens.
I spent 5 years raising free-range chickens for eggs when I was younger. We vaccinated all newly-hatched biddies as soon as they were strong enough to withstand a little handling. Ususally, this was done in a supply shed where all our medicines were kept, and as such, whoever was unlucky enough to be in charge that day had to go out to the run and capture as many of the fuzzy little bastards as possible while avoiding mutilation at the hands of protective hens. When a hen realizes her offspring is in danger, she puffs up to about 150% of her normal size and fucking wails.
It sounds like bagpipes being played by an epileptic Scotsman who is using an industrial compressor to keep them constantly inflated.
I can't speak for the larger, "fryer" variety chickens, but in our bantams, this sound makes all the other hens take to the air like a squadron of kamikaze bombers and slam into you with suprising force. Fortunately, they don't corner very well (think cow in a shopping cart), so it's fairly easy to sidestep them.
Still, the first time I provoked a cucco in OoT, I couldn't help but sympathize with poor Link.