I had a chance to take a bobcat with my bow last year but at the last minute, I couldn't pull the trigger, so to speak. I had plenty of reason to; the stupid thing was chasing squirrels around my stand and scared off a bunch of deer in the process. After it chased all of the squirrels up into the trees, it happened to look up and saw me. It stood there for a while shaking it's little bobtail looking at me and I stood there (in my stand) at full draw but I decided not to take it's life.
The bobcat had every right to be there and I felt who was I to take his (or hers) life just because I was irritated at him. He was just trying to survive like every other animal in the woods and I feel, if I'm not going to consume the animal or it's not threatening me or my family then I have no right to kill it. Bobcats are still somewhat rare in Northeastern Missouri and I doubt they have much of an impact on the deer or turkey population so killing them in the name of wildlife management is BS.
Mr Deer Hunter, I doubt bobcats are killing off your grouse. I'd be more inclined to think a combination of a wet spring and summer, a crapload of bird-killing hawks (they're everywhere where I hunt), a decline in suitable habitat and feral cats (I kill those) are impacting you grouse population. I know that these factors have decimated the quail population in NE MO, so much so that during a typical quail hunt, I'd be lucky to see 1-2 covey's a day where we used to see 10-15.