I could go through and 'like' every post by @LittleLebowski, but that would get a bit repetitive. @RevolverRob summed up pretty much anything I would want to say as well.
I remember when this exact topic came up on another board a few years back; a farmer/rancher out west had a pile of coyotes that caused a stir of emotion. What usually comes out are the people who work with and rely on animals for livelihood and those who view animals solely as companions. A different mindset is required for each point of view and many people can't/won't reconcile this.
The next step in this will be discussing putting down large/wild cats..