That's because birds are extremely sensitive to the air; it's how the phrase "canary in the coalmine", or just "canary", originated. The dosage required to kill a bird is a tiny fraction of that needed to cause a human to perceive anything.

That said, pyrolysis of fluorinated compounds does release very toxic substances, HF among one of them. On the other hand, the tradeoff is that below those temperatures at which they start degrading, they are extremely inert.