A short (and correct) answer for why people look in Central America is because of the long-held belief that Joseph Smith wrote the articles in the 1842 Times and Seasons that linked the Book of Mormon to Central America, even flat-out claiming that Zarahemla was Quigua, Guatemala. Some scholars have hedged on that, claiming instead that Joseph, as the acting editor, merely approved the articles. Others have sought to prove Joseph wrote the articles.
It's a reasonable assumption, so I can see why people have stuck with it for all these decades. However, I think most historians agree that recently uncovered historical evidence about those articles, points to Benjamin Winchester, William Smith, and W.W. Phelps as authors/editors of those articles. Joseph didn't know about them until after they were published in the newspaper.
To their credit, some Mesoamerican advocates are saying those articles have nothing to do with the Mesoamerican theory. This is a welcome change. Anyone can read the seminal books and articles citing those articles and observe the ongoing presentations by Mesoamerican scholars claiming Joseph wrote the articles, but presumably that rationale is fading into oblivion.
So let's set aside the Times and Seasons articles. Why else would any Latter-day Saint look to Central America to find the setting for the Book of Mormon?
One obvious answer is the same one that motivated Winchester, et al, to write the articles in the Times and Seasons; i.e., to answer anti-Mormon arguments. In the early days, anti-Mormons claimed Joseph copied the Book of Mormon from View of the Hebrews or the Spaulding manuscript. Moving the setting of the Book of Mormon to a limited geography in Mesoamerica refuted those allegations.
Again, this is a reasonable response to the critics. It may be a major, but largely unstated, motivation still today. But since it's unstated, I can't address it here.
What other reasons are there?
As near as I can tell, the limited geography Central American theory originated with RLDS scholars in the 1920s. Eventually LDS scholars embraced it. The rationale had to do with assumptions about distances and culture.
Tomorrow I've scheduled a post about expectations based on the text, but for now, let's look at a typical rationale for Central America. This one is from fairmormon and it is a fair summary, no pun intended. I think it makes sense if you accept the underlying rationale. It's as good an explanation as I've found, and I have no problem with people believing this. It's definitely one way to view the world.
Following are some of the geographic criteria from the Book of Mormon text and how those criteria are met by Mesoamerica:
• Mapping the internal geography of the Book of Mormon requires that the land be hourglass shaped.
• Writings. Mesoamerica is the only place that appears to have had a sophisticated writing system during Book of Mormon times.
• Advanced cities and fortifications. Archaeology confirms such cities in Mesoamerica in Book of Mormon times.
• Rivers must be the right size and in the right portions of the land (we find such correlation in Mesoamerica).
• The Book of Mormon suggests a temperate climate (for growing such things as “wheat” and “barley”) and never mentions snow or cold in a New World setting.
• Both Book of Mormon cultures and Mesoamerican cultures had developed agriculture and commerce.
• Volcanic activity and earthquake zones.
At first glance there appears to be a problem with Book of Mormon directions and the layout of Mesoamerica. Whereas the Nephites generally used terms such as “northward” and “southward,” the hourglass shape of Mesoamerica runs northwest and southeast. How could an intelligent people like
the Nephites get cardinal directions wrong?
In both Mayan and Hebrew, north means on “the left hand” and south means “on the right.” Studies indicate that some people in Mesoamerica called the Pacific Ocean the “west sea” and the Gulf Coast the “east sea,” just as done in the Book of Mormon. Even some European conquerors used directions
similar to those used in the Book of Mormon when they wrote about their travels in Mesoamerica.
Systems for labeling directions in ancient times varied by thousands of different schemes and were generally arbitrary systems designed by individual groups to deal with their unique geographical and linguistic situations.
To put it simply, the directional systems of some ancient cultures were not based on the same cultural principals as ours. Thus, a Mesoamerican geography for the Book of Mormon is not problematic when considering cardinal directions.
If anyone has a better explanation for why people are looking in Mesoamerica, I'd love to know about it so I could add it here.