It's not a perfect analogy. Turning stray cats into mittens is a sustainable industry in itself. If you can sustain a groundhog mitten industry, so much the better. But we're going into this assuming that you want the fields for the fields themselves, and we all know you just can't butcher strays fast enough to be rid of them. Another solution is needed - I for one don't think plinking them with a .22 is going to work either.
A .22 definitely won't work. They have thick fur and fat that you need to be able to break through from a distance. Our preferred method is 7.62 mm FMJ rounds shot from an M14 at 200 yards... and yes, it does keep the fields fairly clean because they usually nest in an area and stay there for life. Shooting the ones in the fields does keep the ones who claimed that plot from coming back. The do however populate the woods nearby, so it's a never ending task of hunting/waiting them out. It requires laying silent for long periods of time because their hearing is quite good.
And they ARE bad for farmers and fields. They eats the roots and plants and are better served as fertilizer. They will also attack anyone near their nests, so a farmer out inspecting fence lines or crop growth could be attacked and bitten.
I was only arguing this, not because I was justifying guns [though they are cheaper than rodent bombing the entire field...] but because guns can be useful for things other than killing people as well as being for sport/fun. Hunters do not always hunt for food. They also hunt to control the populations of wild animals and for the challenges that it poses. The overall goal is not total genocide. Hunters and farmers are likely more conscious of nature and wildlife than the people in this thread who think guns are only good for gangs of criminals.
That's usually not contested by the population though, because it serves a purpose. Only the absolute fringe extreme pacifists have a problem with it.
My main argument is that automatic weapons are not deadly in the right hands and you are "punishing" all of society for the mistakes of a few people who would rather do harm with them than use them for entertainment purposes. There was a Mythbusters episode where they had a minigun and were trying to cut a tree in half with it. It didn't work, but they themselves claimed it was fun as hell to shoot. There is entertainment to be had in a controlled situation. Sanctioning this control off to the government seems to be your only accepted solution, but my argument is that anyone willing to pay the cost of the gun and shells (quite expensive in quantities that are needed for such a weapon) should be able to own and fire it on their own property for their own entertainment purposes (as long as those purposes don't infringe on the rights of another person to live.)
The law of the land is quite clear in that regard. People have rights and anyone infringing on those rights is breaking the law and should be stopped. I have no problem with that, but you seem to. You would rather say that people should not have a specific right, no matter what.