The name soccer came from Britain, not the US. It was used to differentiate Association Football (soccer) from Rugby Football (rugby). Ireland, South Africa, Australia and New Zealand all still call the sport soccer. Even in England, it continued to be a popular name for the sport until the 1950s.

Correct, and most native English speakers are American. That doesn't even account for Canada or Australia where it has also traditionally been called soccer.

The fact that the "F" stands for "Football" in the name of an organization with a French name seems irrelevant.