Basically, the Mesoamericanists say that Nephi prophesied about Columbus, and Columbus visited Mesoamerica, not North America, so therefore, the Book of Mormon setting must be Mesoamerica.
The argument is fallacious on multiple levels, but before explaining why, I want to let Matthew Roper explain the Mesoamericanist position. I don't know whether Roper initiated this argument, but I see it repeated frequently. (In this article Roper was making the case that all of the Americas are the "promised land," so North America or the Heartland is not exclusively the promised land. I agree with him in the sense that anywhere can be a promised land, but his point is to refute the idea that North America is the promised land in the sense that it is where Lehi landed, and I disagree with him on that.)
One prophecy that deserves more attention ... is Nephi’s vision of the promised land (1 Nephi 11–14). Nephi saw the future events that would eventually culminate in the latter-day fulfillment of the Lord’s covenants concerning the seed of Lehi in the land of promise.
And I looked and beheld a man among the Gentiles, who was
separated from the seed of my brethren by the many waters;
and I beheld the Spirit of God, that it came down and wrought
upon the man; and he went forth upon the many waters, even
unto the seed of my brethren, who were in the promised land.
(1 Nephi 13:12)
Latter-day Saints have almost universally understood this verse to refer to Columbus....(I don't know how one knows what Latter-day Saints "almost universally" understand, but the text doesn't mention Columbus. Certainly there have been efforts to link Columbus to this verse, such as a piece by Richard L. Millett that I'll discuss below. But there are reasons to disagree with this spin. Count me in the group of LDS who does not understand this verse to refer to Columbus. But for purposes of these comments on Roper's piece, I'll take his assumption for granted.) Columbus, however, never visited the land now known as the United States (except he visited Puerto Rico, which is part of the U.S.) and never encountered the people who lived there. (Here he makes a distinction based on his claim regarding ancestry of the Caribbean people, but his claim is designed to support the Mesoamerican setting and is problematic as I'll show.) During his first and second voyages, Columbus encountered the islands and people of the Bahamas and the Caribbean, including Cuba and Hispaniola.4 [4. “All the peoples of the Caribbean came originally by canoe from the continent of South America along the chain of islands known as the Antilles, or the West Indies, via Trinidad and Tobago.” Hugh Thomas, Rivers of Gold: The Rise of the Spanish Empire, from Columbus to Magellan (New York: Random House, 2005), 110.] (There are two key points here. First, according to Roper, the people Columbus first encountered were from South America--not Mesoamerica. So his theory about Columbus would lead to Orson Pratt's South American setting, not the limited Mesoamerican setting. Second, Columbus encountered the Ciboney and Guanahatabey people who lived on Cuba; both of these groups had ties to Florida (which is much closer to Cuba and the Bahamas than South America) and preceded the Taino people who came from South America. Because Columbus and his successors slaughtered so many of the people, it is difficult to reconstruct their history. Roper's reference doesn't mention the Florida connection, but other sources do. E.g., Encyclopedia Britannica and these. So it appears that the earliest ancestors of the people Columbus first encountered came from Florida, which is not only part of the U.S. but where we think Lehi landed. So even if Nephi was describing Columbus, the first people he encountered were from South America and Florida--not Mesoamerica.)
On his third voyage he sailed to northern South America to what is now known as Trinidad and Venezuela. During his fourth and final voyage, he encountered Mayan traders off the coast of Honduras and from there continued southward along the coast of Nicaragua, Costa
Rica, and Panama. In his prophecy, Nephi calls those people the seed of his brethren the Lamanites (this is a variation of the Sorenson translation; nowhere does Nephi call the people along the coast of Central America his brethren) and calls their land “the promised land.” Nephi says that the man went forth “unto the seed of my brethren” and that those people were “in the promised land” (1 Nephi 13:12). This suggests that the “promised land” of Nephi’s vision must include not just the United States or North America, but parts if not all of Central and South America as well. (This makes the case for the hemispheric model that the Mesoamericanists have otherwise rejected. Instead, they claim Lehi landed on the west coast of Mexico, which they claim was the promised land Lehi spoke of, on the theory that the entire Book of Mormon took place in about 500 square miles of southern Mexico--an area Columbus never visited. Not only that, but Columbus was not the first to visit Honduras and Nicaragua; it was only after his brother Bartolome told Columbus about his visit there that Christopher decided to make another voyage there. The Mesoamericanist thinking on Columbus is a mess. Because they reject the North American setting, the Mesoamericanists reject not only the concept of a "promised land" inhabited only (or even mainly) by Lehi's descendants, but they also reject the verses in the Book of Mormon that describe the setting as exclusive (e.g., 2 Ne. 1:8) because they think Lehi landed in the middle of a long-established civilization that completely absorbed the Nephite/Lamanite culture and people, to the point that there is no trace of Book of Mormon people (or at least their DNA) remaining there today.)
Roper's not the only one to frame the Columbus story as support for Mesoamerica. Here's Brant Gardner,in his critique of Wunderli's book that criticizes the Book of Mormon. (BTW, it's interesting that Wunderli also adopts the Columbus interpretation of 1 Ne. 13:12).
Here's what Gardner writes:
Wunderli is correct that the choice land seems to include the lands of the Nephites and the Jaredites, but Sorenson’s geography places those in a limited area. (Note, this is the point I made in my comments to Roper above.) That the choice land might refer to both does not in itself require a hemisphere. It requires only that it cover the area occupied by the Nephites, the Lamanites, and the Jaredites.
How accurate is his [Wunderli's] conclusion that “these passages all clearly, if not explicitly, identify the promised land with North America”? Let’s take the first one, 1 Nephi 13:12. Note that he helpfully includes his reading of the oblique reference of the passage. Accepting Columbus as the reference is not surprising, (presumably because it is what LDS have "almost universally understood) but it is surprising to use Columbus as a proof that the promised land is North America. Columbus arrived in Central America. (Of course, Central America is part of North America. If we're going to consider Central America as a separate region, then we also have to consider the Caribbean as a separate region. You see why Gardner writes this; he wants his readers to think Columbus arrived in the promised land of Sorenson's Mesoamerica. Inconveniently, Columbus never did that, so Gardner generalizes Columbus' voyage to encompass all of Central America. But then his argument boils down to how far, from where Columbus actually landed, is a legitimate extension of the promised land. I.e., since even Gardner has to admit Columbus never landed where Gardner claims the Book of Mormon took place, he argues that it was close enough. But actually, Columbus landed closer to Florida than he did to southern Mexico.) His voyages of discovery were south of North America. (Do you see why it is difficult to follow the arguments of the Mesoamericanists? Central America and the Caribbean are part of North America! Columbus landed both north and south of Sorenson's Mexico setting. He landed both east and west of Florida, but at his closest, he was hundreds of miles east of Sorenson's Mexican setting.) Wunderli never tells us why the reference to Columbus points toward North America. He clearly assumes it, (because by simple definition, Columbus reached North America) but that does not make for a compelling argument. (This shows what Gardner considers a compelling argument; i.e., his argument that Columbus' voyages were "south" of "North America," when every definition of North America includes the areas Columbus visited. Here's a map of North America from 1621, for example.) Columbus never set foot on North America, and if we use him as the arbiter of location we are back to the limited model, not the hemispheric one. As in other places, Wunderli presents evidence contrary to his position. (I'll let you decide whether it is Wunderli or Gardner who presents evidence contrary to his position. The point here is that Mesoamericanists are dogmatic about their theory. They refuse to engage with those who criticize their theory, and they spin facts to support their theory, ignoring realities that contradict their points. No matter what I write, they will continue to make this argument about Columbus. It has been going on for decades.)
NOTE: there is a ray of hope, however. There is a Maxwell Institute publication that raises the Columbus issue. Stephen O. Smoot wrote: "I urge caution with Ash’s identification of Columbus as the Gentile spoken of in 1 Nephi 13:12. Although this idea has most certainly been a prevalent interpretation among Latter-day Saints, it is speculative and cannot be classed as evidence for the Book of Mormon. Ash does give some intriguing details about Columbus’s own conviction that he was being led by divine forces in his explorations, and he mentions the famous mariner’s Libro de las profecías (p. 95). There are, however, risks in constructing an argument based on a fundamental uncertainty." Let's hope this caution prevails over the far more common Mesoamericanist argument.
Alwyn Ruddock, a well-known academic in the UK, claimed to have found evidence that a voyage from Bristol England discovered North America before 1470--well before Columbus--but she never published the book she promised. The Cabot project is pursuing this area of research. On Cabot's first known voyage to North America in 1497, he did not encounter any native people, but if the earlier voyage did, it would replace Columbus both as the first to "discover" the new world and the first to encounter people there. Presumably, like Cabot, this would have been somewhere in Eastern Canada or Maine. From a doctrinal perspective, Nephi would have seen the reality of the first discovery, not the most newsworthy. (I don't think the text even requires that Nephi was describing the first discovery. It only refers to a man wrought upon by the Spirit of God, which seems to describe Pilgrims more than these other explorers. And, of course, the Pilgrims came to New England, which is where the plates were found, etc.)
Now, one last comment on Columbus. Here is an excerpt from the Millett article I mentioned above (full link is http://www.bmaf.org/articles/columbus_promised_land__millett).
I don't have time to dissect the entire piece, but I do want to call attention to this paragraph and juxtapose it with some history. Then you can decide what to think about Columbus. (Note: I'm not among those who revile Columbus, seek to eliminate Columbus day, etc. But I also don't think God inspired him to come to America and commit these atrocities.)
"Columbus played an important role in uncovering the peoples and cultures of the Book of Mormon. They had waited for centuries for the Gentiles to find them and to establish a nation whose government would foster and give birth to freedom. With the proper climate established, the way was prepared for the Restoration and for the emergence of the record of the inhabitants of the Americas, the Book of Mormon (see 1 Nephi 13:30–33 and 3 Nephi 21:1–9)."
Hispaniola is a miracle. Mountains and hills, plains and pastures, are both fertile and beautiful ... the harbors are unbelievably good and there are many wide rivers of which the majority contain gold. . . . There are many spices, and great mines of gold and other metals....