Poor cat. I could be wrong, but I don't think bobcats are a pest species & I don't think you eat them. Why kill it?
As for "yotes & cats" hurting the rabbit population, if memory serves rabbits aren't the primary prey of either one, although they will glady eat a rabbit if they can catch them. But I think their diets are mainly made up of bugs, birds, snakes, squirrels & mice/rats.
Now don't break bad on me here. I'm no PETA freak & I support hunting if you're going to eat the meat. But I just don't see the point of killing such a beautiful cat.
Coyotes I can see killing b/c if they become too great in number they can become dangerous. Rabbits & deer I can see killing b/c we eat them. But what did this beautiful cat do? Eat a few rabbits? So kill it? And then brag about it while posing w/ the poor creature's lifeless corpse? That is the epitome of human ego & to me is quite sad ...

"But because of his great love for us, God, who is rich in mercy made us alive with Christ even when we were dead in transgressions - it is by grace you have been saved." - Ephesians 2:4-5