What? Tailfeather is actually quite humane. The hunter who killed the mother and took the eggs was literally exiled from the town because the town does not support that behavior. And yeah there might be some minor injuries to a Chocobo from falling down a 1 meter or so pitfall, but the worst that could happen is probably some bruising. Tailfeather would never actively use a method of capturing Chocobo's that does serious harm to it since the birds are captured to be sold as riding and racing Chocobos. It is unfortunate that you have to put down a Chocobo. But when it's effecting your business and putting human life at risk, it needs to be done. A humans life is more important that a Chocobos.