So your argument is "we should shoot them because they're mean?" I don't think you should hold those mountain lion's behavior against them, they're just trying to
survive, right? It's not like big cats are involved in a violent drug cartel or a barbaric radical religious movement. They're just trying to not starve to death or be killed by another competitor on the ecological survival paradigm. I'm not sure there's a "non-vicious" way to do that. If you want to put forward the ethos that violent, aggressive animals are more justified as hunting trophies then I think man should be on the table.
I don't get all offended by pictures of a couple of dudes preening over a dead animal, if that's your outlet for expressing manhood go for it; delight over ending another life seems to excite many, but it's a fetish that I don't share and if I want to make fun of those that do...
Go wank over your corpse-trophy and deal with it, trophy hunters.