Okay, where to begin? There is actually much to learn in this joke. Take my random comments in that spirit. Remember, you asked for it!
First, let's discuss patterns of jokes. Jokes often have three repetitions of the same phenomenon (or at least similar phenomena). The first two establish a pattern. The third occurrence either follows the first two with a humorous twist, or else it deviates from the pattern in a humorous way.
In the present example, the first two repetitions establish this pattern: the suitors of the daughters of the farmer have names that rhyme with the names of the daughter AND rhyme with the activity they propose for the evening ("im Freddy, here to see Betty, we are going out for spaghetti," etc.) The third suitor's name is Chuck. We are primed (by the first two occurrences) to think of activities that rhyme with Chuck. The activity that comes to mind is what the
backronym "Forming Unlawful Carnal Knowledge" refers to. That is, the first step in making babies. (To all of you cunning linguists out there, I am well aware that the etymology of the word in question, that is, the one that rhymes with Chuck, is NOT derived from "Forming Unlawful Carnal Knowledge," but just trying to beat the censors.) The Farmer is alarmed by the proposition of his third daughter copulating with Chuck, and so he kills him to prevent this extramarital copulation. (Isn't that hilarious! Get it!?
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While we are dissecting the frog, let's dig deep into "Farmer's Daughter's" jokes. I don't know if "Farmer's Daughter's" jokes are regional or not, as you suggest, but I kinda doubt it. I grew up in a much more urban area than where you live now, but not that far from it, and we heard these jokes as children. The crux of them is that either male strangers or male neighbors are thrown together with the daughter(s) of a farmer. The males wish to copulate, and the daughter (generally) is receptive; the farmer tries to prevent the copulation. The humor derives from either the means that the suitor uses to succeed, or the means that the farmer uses to thwart the copulation.
Let's dig deeper. Why "Farmer's Daughter?" Why not "Accountant's Daughter?"
Well, the concept of monogamy probably arose at the same time as agriculture, that is, only some 10,000 years ago or so. Agrarian societies were the first in mankind's history where inheritance of goods, in this case, land, was important. Before that, for the first 200,000 years or so of modern humans' existence, it didn't really matter whose child it was in most cultures, so the emphasis on monogamy was not as prevalent.
If you were consigned to monogamy, and you were running a farm, it would be very important that your wife was not barren. That is, it was very important that your marriage would result in many children, so that you would have sufficient labor to run the farm. Thus, it was very, very common in nominally monogamous agrarian societies to take proposed mates on a "test run." If the woman got pregnant, then the male knew she was fecund, and marriage was favorable. If not, well, time to try planting in a different field.
The father of the woman in question, of course, had a different interest. His interest was in marrying off his daughter (who had limited value to him on the farm) to a prosperous neighbor-farmer, whether or not she was fecund. In fact, his interest was aligned with marrying her off before her fecundity was determined. Thus, he had an interest in preventing speculative copulations. I believe these are the reasons that the jokes revolve around "farmer's daughters" and not some other profession, but this is my own speculation.
Okay, is the frog completely dead yet?
