I understand that in the "Columbian Exchange," one of the things brought over from the Old World was smallpox, which killed the vast majority of the native population. I get this is because that was a new disease to the natives, so they had none of the resistance/immunity that Europeans did.
How come the opposite was not true? I'm recommended to have certain vaccinations to travel to South and Central America just being from the United States. How did none of the conquistadors/explorers/pioneers not bring back any deadly diseases on the scale of what happened to the natives?
Simply put, the Old World wasn't being colonised by Europeans at the time. The death toll from disease during the Columbian Exchange was a direct result of the dislocation, violence, warfare, enslavement and famine caused by European encroachment on Native American land and resources. /u/snapshot52 has an excellent primer on the subject in this Monday Methods thread - you can scroll down to 'Methods of Denialism: Disease'.
In addition the answer linked by u/Iphikrates, consider these two threads
Regarding "New World" diseases: When Europeans brought diseases to the new world, how come Europeans themselves didn't get sick from diseases specific to the new world? written by u/anthropology_nerd
Regarding the extent of Old World diseases in the New World (it has often been overstated): Disease in 'The New World' with answers by u/Reedstilt and u/anthropology_nerd