This is a bit of one of those "why isn't x taught more" questions.

Firstly, the Transatlantic Slave Trade is obviously going to be taught more thoroughly in American schools because it directly impacts American history (both United States and the Americas as a whole) in a way the Black Sea slave trade did, even though it occurred at the same time. I would say that this doesn't necessarily hold for Ukrainian (and to a lesser extent Russian) history as taught in schools, as this was a major part of early modern history in the region.

With that said, there are a few things worth noting about the Crimean Slave trade and its raids across the "Wild Fields". One, while this period was known for wide-ranging slave raids (up to an including successful raids on Moscow itself), the Crimean Tatars and Nogais were to a large extent inheriting existing slave trade routes that had operated for centuries, whether at the hands of Genoans, or Rus', among others.

While not downplaying at all the fact that slaves moved across the Black Sea were indeed slaves and mostly had very harsh and miserable fates, there are some noticeable differences from the Transatlantic Slave Trade. The Transatlantic trade was almost exclusively a one-way intercontinental trip to vast plantations in the Americas, which in turn produced commodities for re-export to Europe. These chattel slaves, where they survived and formed communities, we're in essence treated as not just a social but racial underclass, hereditary and easily visually recognized. Ottoman slavery wasn't quite the same, and slaves could be ransomed and released (ironically this did happen on a couple of occasions in the Americas with African Muslim slaves at the request of Ottoman sultans), could convert to Islam, could be freed, and could reach relative heights of power. Hurrem Sultan or Roxelana was a slave from Ukraine who rose to become the legal wife of Suleiman the Magnificent and one of the most powerful women in the Ottoman Empire. This was clearly not the norm, but nevertheless even this sort of winning the lottery was essentially unthinkable in the Americas for slaves.

Another major difference with the Black Sea is that the trade wasn't strictly one-way. Muscovy had legal slavery until 1721, and while the Crimeans often took slaves in raids, there were plenty of Russian slave markets for both domestic and international sales, and the Crimeans occasionally made purchases there. The Muscovites/Russians in turn took and kept their own slaves, whether through conquest of other peoples, or sales into slavery to pay debts, and was occasionally even a destination for the international slave trade - one famous example being Alexander Pushkin's gread grandfather, Abram Petrovich Gannibal, who was enslaved in Central Africa, transported to Constantinople, and ultimately sent to Peter the Great's court, where he was ultimately freed.

Again, none of this is to deny that slavery across the Black Sea in the 16th-18th centuries was a massive and miserable affair. But it was both part of a much longer-standing trade, and also had unique characteristics and interactions on both sides of the Sea that make it not really a great analogy to the Transatlantic Middle Passage. Both are very different histories and treating them separately avoids doing the victims of both trades a disservice.

This is a good question. Part of it is because of interest and the other part of it is due to sources. It is much easier to research the Atlantic slave trade because there are more records and more countries were involved in languages commonly taught in America. Crimean slavery covered Russia, Poland-Lithuania, and the Ottoman world. Atlantic slavery also had direct impact on the colonial Americas. The slave trade in the Crimea and Ottoman Empire was concurrent and linked with the global trade. In addition, far too often popular histories, textbooks, and journalists try to create a false dichotomy between Ottoman and Atlantic slavery. Typically this is done by pointing to the janissaries as a "slave" class. The Ottoman word kul literally means slave, yes, but the janissaries were a part of the elite. There were also many chattel slaves in the Ottoman Empire comparable to the status of African slaves in the New World, although the empire did not have an institution comparable to the early modern plantation system that created the demand for slaves. Ottoman sources that I have researched are also a bit vague when it comes to enslaved people as well and European accounts do not have an insider's impression. John Smith's True Travels give a good impression of the trade that ran from the Crimea to Central Europe, but he was also captive only for so long.

As a historian I would like to see more emphasis on the early modern slave trade as a global phenomenon emphasized a bit more, although most fields are moving to a transnational/international direction so it is happening in academia.

The simple (and disappointing) answer is that it's too obscure and complicated a topic for American textbooks and non-university education to touch and doesn't have relevance for the history of the United States.