I understand you have a very strong opinion on this and can imagine why, but I don't believe that dismissing other peoples' points of view while repeating your own is ever going to make someone suddenly see the light.
For example, the context to your above questions is the law, which varies by location. And we make up the laws that give us the right to exploit the planet, and animals, and other people so they're probably not the answer you want anyway.
Poeple don't wake up in the morning wondering how they are going to ruin the planet today. They might wonder how to protect their birds. They might even believe having their own birds and killing a predator once is a while is better for the planet overall than buying industrial meat from the store. A better question than "what give you the right" might be, what can be done to make it easier to protect the birds in a way that discourages killing predators. We have non profits helping fund electric fencing and managing attractants for people to reduce conflict for example. That has worked way better to save bears from being shot around here than treating people like they're a child by wagging a finger saying this is a big no no, find another way.
Also, note that I fundamentally I agree humans should be caretakers of the planet or at least leave a small footprint and not exploit/destroy it, though I have a more moderate/pragmatic stance, so I'm not going to argue further.