I'm not a hunter but what do you all suggest? These animals have killed and eaten children. They go into towns and kill dogs. Just let the population grow and grow?
http://www.huffingtonpost.com/2014/09/07/mountain-lion-attack-cupertino-california_n_5781858.html
http://laist.com/2014/02/03/mountain_lion_attacks_man.php
here is the thing, did that particular mountain kill anybody?
Yes, they attack folks, And I believe usually from behind, as they are ambush predators. So, that should tell you something about the people that get killed.
There was one woman who was killed, she was jogging, and if I remember correctly, she had headphones on.
There is a delicate balance that must be maintained. Predators like mountain lions, if they attack humans, should be captured and moved. If you can find the individual one, kill it, don't kill all of them. If anything, they are looking for a food source, and humans and dogs/cats are quite easy prey.
They wouldn't be preying on us or our domesticated animals if they had a viable source of food. So, you have to figure out what have we done to their food source. And of course our ever encroaching into their territories as well.