There are many reasons to kill coyotes.
The short answer is yes they cause problems for ranchers and cattle farmers. A cattle farmer I know who lives close by with a very small herd lost 3 calves in a month to coyotes, killing his entire year. In the east they've recently moved in and had a huge negative impact on deer fawn survival rates in some areas.
And even if it looks as if some packs are being decimated, there is virtually nothing that hunting does to their overall population. Hunting doesn't even begin to affect their overall numbers. Even locally, more coyotes will move in within weeks and establish themselves when others are killed.
You can read more coyote predation on fawns at
Why Deer Hunters Should Be Coyote Hunters | horns and horns. As a deer hunter, you might even feel the desire to kill a few yourself after you read the science showing how negatively they can affect deer herds, especially in places where deer have never had to worry about coyotes.
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