Seems to me that the conventional wisdom is that farmers inherit, that the son (almost always the son) inherits the farm and that's where farmers come from. I say "conventional wisdom" although I really mean the presumption in history. Once it was true, of course. If 90-95 percent of the population is farmers, as in colonial America, then inheritance is the logical answer.
The economists had the concept of the "agricultural ladder", where a man worked his way up from day labor to sharecropper to renter to owner. That may have worked in the 19th century, but I think maybe its prevalence is overestimated. In the case of my family, my paternal great grandfather, my maternal grandfather, and my father all moved onto farms aided by money from other occupations or sources (preaching, carpentry, and family, respectively). That's a small sample but it's easy for historians to overlook, because there's no statistics to prove or disprove this.
Today it seems that there's a reasonable flow of people from other occupations into agriculture, particularly the "food movement" end of agriculture: the organic farmers, the community-supported agriculture, the niche products of wine, goat cheese, semi-exotic crops.
This interview with an organic farmer in Grist is interesting, covering many aspects of modern food movement farming. Implicitly it's directed towards people coming to farming, not inheriting farming. There was also a recent article in the NYTimes on the graying of the organic movement, which made the point that children of some people who came to organic in the 60's and 70's had no interest in continuing on their parents path.