This isn’t really remotely a compelling argument, and let me explain why.
I grew up deer hunting, and hunting in general. I have, personally, shot multiple deer, and field dressed more. And though I haven’t gone in a decade, most of my family does.
It is not financially cheaper than buying meat.
The cost of the deer license in Illinois was about $25 a deer, or $45 for a pair. Not a bad deal if that’s the only cost.
But it’s not.
And you’re not guaranteed a deer.
There’s the cost of the ammo, the shotgun, cost of food and lodging for the hunting grounds if you aren’t already living on a farm, camp, scent markers, boots, hand warmers, and on and on. My grandfather owned a cabin in southern Illinois we went to. Given all that my father estimated that it cost between $3-500 per deer he shot, when it was all done. For between 80-150lb of meat.
Now certainly if you live on your own farm and can just walk out a quarter mile in the morning, some of that cost vanishes. But the reality is it still is likely to cost a not insignificant sum. Easily $100 if you have absolutely zero costs other than those directly related to shooting the individual deer. That’s no new clothing, scent masking, calls, shotgun, etc.
If you actually add up the sum total costs, even for someone living in the country hunting their own property, the cost per pound is still going to be higher than buying a pack of chicken or pork at the grocery store.