I cannot stand to let something suffer.
So what about being caught by the foot means the fox was “suffering”?
Just going with what the OP said about putting the fox out of its "misery". I'd say misery and suffering were about the same thing.
Sucks to be a wild animal. They rarely die of old age and every other way is hard. I don't mind killing something, but trapping it in a leg trap can induce a lot of suffering on the part of the critter if by nothing else being held in place and eaten alive.
