Rips (1975) showed that people were more likely to expect a disease would spread from robins to ducks on an island, than from ducks to robins. Now this is not a logical impossibility, but in a pragmatic sense, whatever difference separates a duck from a robin and would make a disease less likely to spread from a duck to a robin, must also be a difference between a robin and a duck, and would make a disease less likely to spread from a robin to a duck.

Alas, the same argument shows that diseases are equally likely to spread from Spaniards to native Americans as the other way around. However, that turned out to be completely wrong: the Spaniards had an extended symbiosis with domestic animals, and had developed immunity to most of their diseases - while the native Americans had no such symbiosis with large animals. They were vulnerable to the germs the Spaniards brought with them, without their germs causing the Spaniards any problems.

The flaw in the argument is that a difference involving a host with a full pathogen reservoir is asymmetric - it makes the pathogens spread away from the reservoir, but not towards it.