If you read arguments in favor of the Mesoamerican setting for the Book of Mormon, you see they basically fall into one of three categories:
2. Appeal to Experts.
3. Word thinking.
None of these are persuasive to most people who have any awareness of the North American setting for Book of Mormon geography. That's why the LDS scholars and educators who promote the Mesoamerican theory suppress information about the North American setting as much as they can, and fight against it when they have to address it.
The one thing they will never do is give their readers and students a fair and open side-by-side comparison.
Here's why their arguments fail.
1. Analogies, such as identifying "correspondences" between Mayan and Nephite culture, are imperfect because they focus on one feature while overlooking--or hiding--others. The issue becomes the quality of the analogy instead of the merits of the underlying substance of the Mesoamerican theory and the two-Cumorahs idea it is based on.
2. Appeal to experts is not persuasive when there is at least one expert who disagrees, and in this case, every non-LDS expert disagrees with the LDS Mesoamerican advocates regarding the correspondences to the Book of Mormon. Appealing to experts always raises the question of who is an expert and who gets to decide what experts are credible in the first place. In this case, a handful of LDS Mesoamerican scholars provide information and analysis that a much larger group of LDS scholars and educators rely upon to promote the Mesoamerican theory, but the latter group are not experts in Mesoamerica. This leaves the LDS Mesoamerican scholars as a tiny minority of all Mesoamerican scholars in seeing the Book of Mormon as a Mesoamerican document. At the same time, other LDS scholars find the North American setting to be more in harmony with the textual descriptions as well as relevant archaeology, anthropology, geology, and geography.
In the past, many Mesoamerican promoters relied on Church history experts who cited the anonymous 1842 Times and Seasons articles, but that argument has faded in the light of new understanding of Church history. Actually, the Church history argument has turned sharply against the Mesoamerican theory, at least to the extent it relies on the two-Cumorahs claim, now that Letter VII has been more widely acknowledged.
In the LDS context, the appeal to experts is even less persuasive than normal because by definition, most LDS defer to the prophets and apostles as the experts regarding Church doctrine, including Book of Mormon issues. Joseph Smith and Oliver Cowdery are by far the most authoritative sources on the Book of Mormon because of their roles in the translation itself, their interaction with numerous heavenly messengers, and their status as Apostles and President and Assistant President of the Church. The two-Cumorahs theory is a repudiation of Joseph and Oliver, and therefore most LDS people apply a heavy burden of proof on LDS scholars to overturn what Joseph and Oliver taught.
3. Word thinking. Some LDS scholars have sought to support the Mesoamerican theory by adjusting the definition of terms. A classic example is Joseph Smith's identification of the remnant of Lehi's people as "the Indians that now inhabit this country." Joseph was writing to Mr. Wentworth, who, like Joseph, was a resident of Illinois. The two men lived about 200 miles apart. Both lived in the United States.
But to justify their Mesoamerican setting, LDS scholars have interpreted Joseph's use of the word "country" to mean the entire hemisphere, or at least an area that encompasses Mesoamerica, which was 1,700 miles away and in a different country.
The LDS scholars and educators also use word thinking to say Joseph mistranslated the plates by dictating horses when he should have dictated tapirs, towers when he should have dictated pyramids, etc. They also engage in work thinking with their circular arguments about volcanoes and geographical features.
This type of word thinking is unpersuasive, especially when combined with the other two categories.