Why hunt with airguns? Outdoor writer and airgun enthusiast Jim House states it best:
As urban sprawl continues, some types of hunting are conducted in somewhat congested areas. Even a rimfire firearm chambered for the .22 Long Rifle fires a bullet that can carry up to a mile so taking a shot at a squirrel in a tree may result in a bullet going a long way unless it strikes the target. However, a pellet fired from even a high powered airgun has much shorter range and there is much less potential danger should the pellet miss the target. Because many people do not like to hear the report of firearms near their dwellings, places of business, or farm animals, hunters using firearms may not be welcome in those areas. However, the use of a quiet, efficient air rifle may cause much less concern so that the hunter using an air rifle may have opportunities to hunt in areas where the use of a firearm would not be allowed.
Many hunters choose to use some sort of equipment that has limited capability just for the challenge. This situation applies to archers who choose to use a traditional recurve or long bow instead of a high tech compound bow. Another illustration is the hunter who chooses to use a muzzle loading rifle instead of a modern high powered rifle chambered for a centerfire cartridge. Quite naturally, hunters looking to test their skill and technique often elect to hunt with an air rifle that has lower power and more limited range than a firearm affords. The additional challenge makes the hunt more satisfying and exciting even if the bag contains less game. Hunting is practiced for the sport rather than for the spoil. As hunting areas decrease, going afield with an airgun provides the challenge without some of the concerns that accompany the use of a firearm.