The great Frederic Bastiat was an eloquent enemy of Latin in the curriculum.  In the Middle Ages, he admits, “There were only
Latin books; writing was done only in Latin; Latin was the language of
religion; the clergy could teach only what they had learned–Latin… Hence, it is understandable that in the Middle Ages education was
confined to the study of the dead languages, quite improperly called
the learned languages.”  But, he asks:

Is it natural, is it good, that the same should be true in the
nineteenth century? Is Latin a necessary means for the acquisition of

Knowing a language, like knowing how to read, means having possession
of an instrument. And is it not strange that we should spend our whole
youth in making ourselves masters of an instrument that is good for
nothing–or not good for much, since nothing is more urgent when one
begins to know it than to forget it? Alas, if one could only forget as
quickly the impressions that this wretched study has left!

If that condemnation isn’t clear enough, Bastiat later adds:

The study of Latin is much praised as a means of developing the
intellect. This is purely a conventional judgment. The Greeks, who did
not learn Latin, were not lacking in intelligence, and we do not see
that French women are deprived of it any more than they are deprived of
common sense. It would be strange that the human mind could not be
strengthened without becoming perverted.

Modern educational psychology backs Bastiat up.  Here‘s a nice short summary of the century-long literature.  Studying Latin does not boost verbal IQ, nonverbal IQ, math scores, or native language performance:

E. L. Thorndike (1923) did not find any differences in the science and mathematics achievement of higher education students who learned Latin at school and those who did not. In the Nuremberg longitudinal study on learning Latin, Haag and Stern (2000) intended to find out whether these findings could be confirmed in Germany about 70 years later… To control for possible selection effects in foreign language choice, data on intelligence, school grades, and interests were collected at the first measurement point at the very beginning of Grade 5, that is, before the participants started to learn their first foreign language. No differences were found in either verbal and nonverbal IQ or grades in German and mathematics between the 115 students who started with Latin as their first foreign language in Grade 5 and the 93 students whose first foreign language was English.

Followups at the end of Grade 8 similarly found, “No significant differences… in deductive and inductive reasoning or text comprehension… among students with 4 years of Latin, 2 years of Latin, and no Latin at all.”

None of this should surprise you if you’re familiar with the literature on Transfer of Learning.  Contrary to teachers’ wishful thinking, learning is highly specific.  The most promising place to look for side benefits of Latin education would be in the acquisition of other Romance languages.  Even here, though, Latin turns out to be less helpful than French, a language hundreds of millions of people actually use:

Students who studied Latin at school were less well prepared for learning Spanish than their contemporaries who had learned French at school. The superior performance of the French group was particularly marked in the correct use of grammar rules and was also obvious as a trend in vocabulary skills. The negative transfer effects of Latin on learning Spanish, which became apparent in the analysis of grammar errors, suggest that accessing Romance languages by way of Latin may not only be a detour but may also be
a complication.

The Panglossian labor economist might object, “If teaching Latin wasn’t useful, the market wouldn’t reward it.”  To which I reply, “If the fact that the market rewards Latin isn’t strong evidence in favor of the signaling model of education, what is?”