There are many reasons to hunt coyotes.
While you can not blame them for doing what comes naturally, they do need to have their populations controlled like many other wild species.
For instance, coyotes ate my neighbors Jack Russels, all three of them. Nothing left but a little blood. While I do not fault the coyote, there is a problem when they begin to over- populate and look for easier meals due to scarce resources.
Some might say we have encroached on their home ground, but this area is very sparsley populated and that is not the case in this instance. There is very little infringement onto "their territory". When hunting this area, I seldom go without seeing a coyote. I too would take a coyote if the opportunity presented itself. Regulation of a species is far superior to overpopulation and disease.
Just My Opinion,
Charlie