I know the british made up the word "soccer", but I've never met or heard any british person ever call it that. Nowadays it's just a term a minority of country uses instead of saying football.
Virtually every sport ever has been called "football" at its inception. Ancient cultures that didn't interact with each other didn't have much need to organize them and make sure everything had a different name. As more games were invented, more names were too. The UK had "Association Football" and "Rugby Football", and I guess that was too redundant, so Association Football became soccer as slang. Then some of those Europeans floated on over and broke some things and made a new country while still calling the game soccer, and with that name I guess they didn't need to call the other one Rugby Football, so they just slanged that one down into football.
Some hundreds of years later I guess for the first time ever in history two different countries developed linguistically in different directions, so I guess we'd all better constantly make a big deal out of it since everyone knows the minority is always in the wrong for being different.