Big cats have a place in our world BUT it shouldn't close to habitation. Plenty of game for a cat to live on so they shouldn't be allowed the opportunity to predate livestock or threaten humans.
A few years back, a cougar took up residence near an Amish community in Macon county MO. Amish tend to have an assortment of small animal type livestock and the children often walk or ride pony carts to school so a cougar setting up shop in the area is/was disturbing. They formed up in the typical 'fox hunt' surrounding the area where the cat was suspected to be hiding and dispatched the cat. MDC got all upset but public opinion and publicity overcame the state's hissy and it all settled down.
What does this have to do with 'Mountain Men'? Anyone who thinks that chasing a cat for a couple of hours will make it leave the area has no clue about cougar behavior.