Why didn't it work symmetrically? Shouldn't the diseases going the other way have wiped out Europe? The only major disease I can recall coming from the Americas was syphilis.
Or in simplest terms, Old World germs were way nastier. (Contrast: African settlement.)
Eurasians/Africans evolved an immune system capable of fighting infectious diseases because for thousands of years they lived in close quarters with domesticated animals and other people.
American Indians had few domesticated animals (only Llamas and Alpacas, I think), minimal over overcrowding and hence had few infectious disease. This caused them to be tall and healthy by contemporary Eurasian standards, but also made them prone to illness.
For much the same reason, I got food poisoning twice in two weeks in Egypt but my (Asian) Indian girlfriend came away unscathed.