Right.
Hunting is a sport and is meant for enjoyment. The possible benefits therefore are: happiness, (meat), (reduced population).
The amount of enjoyment derived from any sport is probably similar (at the very least, I'd contest that hunting provides the most entertainment) so the happiness gain could be adequately satisfied without recourse to hunting.
I accept culls as necessary under certain circumstances, I don't really know the ins and outs of them. An explanation of why they are necessary would be nice (but not necessary).
Hunting, when it is not as part of a cull though, is not an efficient way of gathering meat. I do not agree that it is worth the cruelty on the value of satisfaction derived alone, and I doubt that humanely slaughtering animals that have been bred in farms is more cruel than shooting a deer with a gun. Therefore, I do not accept that hunting brings more benefits than negatives, especially considering the primary benefit can come form other sources.
Lastly, hunting is a barbaric practice that could have damaging psychological effects, from killing living creatures. I personally am proscribed from eating any meat that has been killed either ritually or for enjoyment, and I'm afraid this includes hunting.
tl;dr Don't hunt. Go climbing instead.