If you aren't going to eat it or make something nice out of the pelt or have livestock to protect, why would you shoot one?
For one thing they over populate real fast.
They eat all the local game like rabbits and squirrels.
When thats is gone they start going in peoples back yards and start killing peoples pets that are tied up.
Then there is the raybees thing that is a problem.
Another words in some places they are just like really big rats.
They get in chicken houses and kill chickens.
and kill a lot of small live stock.
Some times they will kill just to kill even if they are not hungry.
And the thought of your small children playing in your yard being attacked by them.
I seen a show where in one town the coyotes were so many they had to have people with guns
standing around a school play ground to keep them from attacking the children.