Same, I've done the same with my cat but with birds,and a frog .

I wouldn't intervene if it was a fox with a rabbit as they need to eat, but a dog or cat who get fed by hoomans, yes I would intevene and regularly shoo next doors cats from the trees in my garden as they are bothering the birds, this is why I could never have a cat :sad:

But you're more than happy to eat a bird yourself no? :conf: