If I recall, in some countries, the only legal guns are rifles--because they can be used to hunt game. Or, to put a finer point on it: some people use a gun to feed their family.
Once you own the gun, ammunition is cheap in comparison to the poundage of meat from deer, wild foul and other small game animals.
Not that I partake in hunting personally (suburban lifestyle), but my home state (of Pennsylvania) has a significant rural population that takes advantage of the large deer population to supplement its caloric budget.
America isn't homogeneous with regard to its distribution of jobs, supermarkets and population.
It's often public land. State or national forests, which are gigantic portions of the US, are generally hunting areas (though state or national parks are usually no-hunting zones).
Hunting is licensed by the states, and is usually relatively inexpensive for in-state residents. People from other states usually pay considerably more for a license. Big game or rarer animals may require special "tags" which come at larger fees and may be limited and awarded by lottery.
There are private game reserves. Georgia and other southern states have massive hunting preserves that can be a mark of old money, for instance. There are similar ranches in the west. And hunting clubs that anyone can just buy their way into.
And, to be honest, there's a lot of what is technically poaching- hunting on the private land of others without permission. That sort of thing isn't all that well policed, though state fish and game authorities are generally pretty tough on completely unlicensed hunting.
"Hunting" in the UK usually referes to chasing about with horses and dogs, "shooting" to pheasants, grouse etc. and if you tramp about mountainsides after deer it is "stalking".
Interestingly enough, in Scotland although most wild areas are privately owned everyone has a right of access - you can wander about pretty much anywhere that isn't explicitly private or where you would cause harm.
My extended family has a modest-sized plot of land in west Pa. where they do farming. It also encompasses some forest though, and occasionally the deer get a little too curious and then my family will get to have venison for dinner for the following month or so.
You have obviously never been to Alaska, where the option to even buy food is non-existent in many areas. Even in areas where you can buy meat, many don't because it is a lot cheaper to feed a family by killing your yearly moose.
"Maybe there are places where it really is cheaper to hunt food with a gun than buy it, but America is not one of them."
This is not true. Where I went to college, there were people in the surrounding area who ate squirrels. Yes, squirrels are edible, and a handful of squirrels can make a meal.
.22lr ammunition is more than sufficient to kill a squirrel, rabbit, or small bird, and you can buy it at 4 cents per cartridge. That means you can get all the meat needed for dinner for 20-30 cents. Excluding food stamps, where else can you get meat so cheaply?
There is another issue with hunting, which I mentioned elsewhere: overpopulation. In many places in America, there are so many deer that they are considered a nuisance species. I live in an area where there are more deer today than there were when Europeans first arrived on this continent. Hunting deer is a form of population control and the limits on how many deer can be taken are set to meet those goals.
Yes, controlling the deer population is important. Deer cause a lot of property damage, and that problem is worsened as the deer population increases.
If I recall, in some countries, the only legal guns are rifles--because they can be used to hunt game. Or, to put a finer point on it: some people use a gun to feed their family.