I would be inclined to address this question along two lines. The first line speaks to the morality of hunting, the second line speaks to my personal aesthetic of hunting.
If challenged by another that hunting was immoral, my reply would be, if eating meat is moral, then my killing deer and eating deer meat is moral. Paying someone else to kill a cow so a beef roast can be purchased and cooked is not morally superior to killing a deer oneself and eating the deer meat. I don't buy arguments that killing the deer is less moral than the slaughter house killing the cow because the killing means of the slaughter house are less painful: relative to causing pain to the deer, certainly the pain caused by the hunter killing the deer is a less painful death than that suffered by the deer in the wild -- being run to ground in deep snow by coyotes, suffering a slow, agonizing death from some trauma, suffering a slow, agonizing death from worn down teeth leading to starvation, a slow agonizing winter-kill death. Deer don't die comfortable natural deaths well fed on their beds. Taking the life of a deer before the natural term of its life is no more immoral than taking the life of a cow before the natural term of its life. Hunting deer provides a positive benefit to society, in that it controls population numbers at a level which is appropriate (limit agricultural damages, limit car crashes and human injuries).
The above addresses, I think the question of morality. Even if moral, however, why do I do it? It would not be immoral to walk barefoot through a pile of cow manure, but that doesn't answer the question of why someone would voluntarily do this. In the case of deer hunting, I voluntarily expend limited vacation time, expend significant amounts of money for non-resident hunting license, expend money on gasoline driving significant distances to the hunting state, rise from a comfortable bed at 4:30 AM, and undergo significant physical discomfort sitting in the cold and dragging a deer carcass up hill. Why? This is a more complicated question. I enjoy the pleasure of eating excellent venison with good wine, but this is not a sufficient explanation of my motivation. If this motivation were essential, I don't think I would go to the trouble or expense of deer hunting. Simply, the experience of hunting -- the modality of being, of existence that I assume while hunting -- provides me with a deeply satisfying and meaniingful connection with my nature. Your PETA friends would not like this, but we human beings are predators. It is our nature to opportunistically hunt, kill, and consume animals. Hunting connects me with this very real and essential aspect of my nature in a way that buying a non-descript slab of meat neatly packaged inside a see-through plastic wrapper in the store does not. I derive immense satisfaction finding my way to my appointed ambush spot -- a spot that my clever brain has calculated is well chosen for remaining unseen by a deer likely to walk within shooting range -- in the dark, to shoot the expected deer cleanly, to recover the dead body of the deer, to properly care for the meat so it does not spoil, to skin and cut up the meat in meal sized portions, and later to cook this meat myself. This is the real thing. I know that what I am doing is the same thing that has been done by hunters before me -- hunters on the frontier of America as it was developed, hunters who paid homage to Artimis the greek god of hunting in ancient greece, hunters such as Orion the hunter constellation, and yet earlier. It is all the same thing, whether using a .25-06 cartridge packed with smokeless powder, whether using black powder and a ball, whether using a bow and arrow, whether using an atlatl and a spear. This is why I am motivated to hunt, to restore my self knowledge and to understand myself better.
