Why can't people stop invading the animal's natural habitat and learn to live with them rather than kill and destroy anything we don't like?
If you have small animals on your property, put a decent fence around your property to keep the pests out.
If you don't want wild animals coming onto your property, don't move into the bush (forest/ wilderness).
Well, I agree in principle. It's often possible to coexist, as we do with the lions around here. Generally they leave us alone and we leave them alone. But at the same time, it isn't that simple. There aren't many fences that will keep out a coyote, let alone a grizzly bear or a pack of wolves. And a lot of livestock is on the open range and can't be fenced in anyway. I'm not for all-out extermination of predators, but sometimes, in the unnatural state of today's world, they get out of hand and need to be controlled. And unfortunately, with wild animals, "controlled" often means "killed."
As for not moving into the bush, everywhere, including Perth,
used to be wilderness. There are just a whole bunch of people, and they have to live somewhere. It causes problems, sometimes. In the case of coyotes, it's them invading populated areas, rather than people moving in on them.
That's the good news, I guess: the coyotes are doing just fine, and despite attempts at all-out extermination, they have greatly expanded their range in the last few decades. That's causing problems, too, because they're moving into areas where the local fauna aren't adapted to them. But I admire them for their survival abilities and their orneriness. Coyotes feature as the clever trixter/troublemaker in the lore of most western Native tribes, with good reason. I can't help but like them.