Language matters. Words change in shape and meaning through years of use, but their origin is carried in history and understanding that is part of a process of social maturity, as language is a net we all hold together. However, words are not innocent, and how we use them can reveal a set of asymmetric relationships that we could decide to accept or not.
In the 19th century, the most popular sport in the world was dubbed “association football” due to the British Football Association in order to differentiate it from “rugby football,” another popular sport in the territories colonized by the empire at the time.
With time, “association football” contracted to “soccer” and “rugby football” to “rugger” or just rugby. It makes sense dropping the “football” from rugby, because people still understand what that is about. But dropping “football” and leaving just “association” did not make much sense.
The term then gained a foothold in the United States, where “soccer” was commonly used to differentiate it from another sport that was in development during the 20th century: American football, also known as gridiron.
Again, dropping “football” from “American football” just didn't work, so the second word was left to describe a sport in which the foot is barely in contact with the ball. That has made many think the sport is a “misnomer,” but that's just the way language works.
The word soccer was later abandoned in the U.K., where “American football” was not that big of a deal, and the same happened more recently in Australia, where the name of the sport was changed to align with rest of the world. But it the word stayed in the United States, where their own version of “football” retained the name.
But that doesn't mean it's wrong, it's just how it works. Languages around the world differ across time, and hence you got dialects. Then, dialects themselves turn into languages in time, before they in turn split into dialects and so on. But that's not the complete history.
The United States of America, for example, dropped the “United States” and began calling themselves just “America,” even though that's the name of a whole continent. And it goes the other way around! You can drop “America” from the “United States” and the rest of the world still gets it! Why? Because the U.S. enjoys a global culture hegemony and is able to spread their terminology through a powerful media machine.
The United States of Mexico, on the other hand, can't do the same. Dropping “Mexico” from the “United States” leaves the country with the name of their northern neighbor, so what's dropped is the first part of its official name, which is more easily distinguishable. At the end, Mexico doesn't enjoy the same cultural distribution channels as the U.S., and therefore the rest of the world doesn't know that the most popular sport in the world, football-soccer, is also known in Mexico as “pambol.”
So, Australia's decision to use “football” instead of “soccer” is related to that: adopting a more universal term for the sport and avoiding the use of a word that makes sense only in another continent.