Okay, maybe that wasn't fair, just frustrating to see this and was unexpected.
Let me say this and leave it be - just because you've done something your whole life and its the way you were taught to handle it doesn't make it right and/or doesn't mean there aren't alternative solutions.
I hunt and trap. I trap foxes (I have a red pelt on my wall). I do nuisance trapping, too. I've helped numerous friends solve predator problems with chickens and turkeys. Controlling predators is useful and important. But there's a lot of stuff I don't do anymore because I was taught a better way or learned more info.
Here's what I do, if you're interested... I target specific animals causing a specific problem if its out of season. Certain species I'll typically check with a warden first to be clear. Then in the season when I'm done deer hunting I trap to stay active and target certain predator species that we're trying to manage. But otherwise, I leave them alone. It's also cool to see them on the landscape and I always want to see them.
Some individuals of the population will never be a problem or pest for you. They'll get really good at finding a certain food source and stay out of your way. You want to keep those around and let them educate the next generation to stay away from your stuff. Studies have shown in coyotes you're actually more likely to have issues if you continually remove older members of the population because younger ones move in and get themselves in trouble.
All that to say, there's a balance to it. These predators are cool animals and they're a necessary part of the ecosystem so it's important to keep a couple hanging around doing their thing. Just maybe give more thought to it when you see them and just.... watch and see what they're doing