In regards to Latin America, and Western slave trade in general, African slave trade began a couple decades after colonies were first established, and is more tied to the introduction of profitable agriculture in Caribbean colonial towns. In particular, the Spanish and Portuguese colonies first used native slave labor, although it wasn't generally referred to as such (there's a whole interesting semi-tangential conversation on this). The origin of black slavery in the West is more a direct answer to the lack of manpower available following the near extinction of indigenous populations via disease, wars, and famine. In particular the Caribbean colonies (see French Haiti and sugarcane) were extremely grueling and required a near constant supply of fresh manpower. At the same time as this need developed, the colonial powers were also expanding into the African continent for both imperial reasons as well as establishing what were effectively pit stop/trade port cities along the various routes to SE Asia. As such, there was easy access to a large, easily captured work force (for example the transit of African slaves to Jamaica in 1517 from Portuguese Ghana, which had already been held for several decades) The "success" of the new slaves (in particular, they didn't die of disease nearly as quickly) caused a massive increase in African slave populations, which then spread. Skipping a few steps, the Columbian Exchange formed and African slave trade became profitable/standardized, thus leading to further expansion of the system. By also paying local warlords for slaves, the European powers also ensured a stable market in Africa and ensured that they had allies on the Continent to avoid unpleasantness.

To the comment in the OP regarding other races, at one point there was also a decent population of Irish laborers in the Caribbean (who weren't regarded as "white" in the same sense as today), but they served more as exploited indentured servants than full slaves, had the possibility (however rare) of making a living, and were quickly replaced by Africans once the slave trade began in earnest.

There also may be a connection to the multi-century Reconquista in Spain against the Moors (north African Muslims) in the choice of Africans as the preferred slave race, as they were often depicted in Spanish literature during and prior to los Siglos de Oro (Golden Age) as barbaric yet strong and heavily masculine. Early colonial Spanish literature (especially Colon and the conquistadors) often compared new lands to what was Moorish territory, as it was the most similar place they knew, thus implanting the idea that African laborers would be successful in the Caribbean and would last long hours in the heat.

On a more meta level with the OP, I'm going to assume based on wording that you're US or NA based, where most history classes are very Eurocentric and thus would emphasize the Columbian exchange over, say, SE Asian slavery. There's also the fact that the African slave trade was absolutely enormous in scale, and heavily international, making it a very easy case study to discuss, in part due to the very real impacts it has had on Africa and the Americas, forming a lot of the race-relations in the modern West.

Preliminary Sources for those interested that I used to double check some info, can back up with more if needed;

H. Adlai Murdoch, A Legacy of Trauma: Caribbean Slavery, Race, Class, and Contemporary Identity

Block, Kristen and Shaw, Jenny, "Subjects without an empire: the Irish in the early modern Caribbean"

Arrelucea-Barrantes, Maribel, "Work, Family, and Honor: Understanding Colonial Slavery in Peru"

Edit: added a couple sources and clarified information based on follow-up verification, rewriting parts of the post for clarity.

I agree with ilTraductor that this is perhaps a symptom of the US education system.

In order to really understand this issue, it helps if one is acquainted with the economics of Pre-Colonial West Africa. The European model for economics, and thus the american one, is tied to the aqcuisition of land. Land is a very important commodity and can even make the difference in whether or not someone is seen as a valued member of society. The West African system simply did not operate that way. Land was not an issue in West Africa and instead the people that WORKED the land became the basis for social status, and riches.

Slavery was the basis for economic achievement, and any one that wished to enter the West African market was allowed to, so long as they brought goods worth trading. The research done by people such as John Thornton really does an excellent job of explaining this system. Europeans tapped into an existing market for a (in the eyes of the people then) valuable commodity that was regularly bought and sold. They did not, and COULD NOT, create this market on their own. This is the very important part that seems to be part of the reason for your question.

Now that I've made some mention of African agency, I'd also like to point out that West Africans also traded with their Northern and Eastern neighbors.

When Ibn Battuta visited the home of the Malian Farba Suleyman, he found in his possession "a slave girl of his, an Arab girl from Damascus who spoke to me in Arabic." His comments don't necessarily denote any surprise or incredulity to find a Damascene girl enslaved in Mali.

Slavery was the trade of the day in pre-colonial africa. As was mentioned above, slavery was the only form of private, revenue producing property. Because of this, Africans would see initially see nothing wrong with trading away fellow africans. But, they would equally see nothing wrong with buying a slave of a different background.

Some great sources on this are 2 books by John Thornton: "Africa and Africans in the Making of the Atlantic World 1400-1800" and "A Cultural History of the Atlantic World, 1250-1820." Also I would recommend "Corpus of Arabic Sources for West African History" by Nehemiah Levtzion and "Senegambia and the Atlantic Slave Trade" by Boubacar Barry.

Theses sources, and my comment, really do tackle the Western part of Africa. Someone else may be able to share more on the different regions.