It ain't bloody hard:
AFL (a misnomer but anyway)
League
Union
Football
Where's the confusion?
The confusion comes from the fact that they're all known as "footy/football" as well. The reason is pretty obvious, as their actual full names are:
Australian Football
Rugby League Football
Rugby Union Football
Association Football
As aside for those who don't know, the word "football" is in all their names because in the 19th century it was a shorthand for pretty well all field ball games played "on foot", which distinguished them from the posh games like polo that were on horseback.
So the confusion arises because every code's fans uses footy/football to refer to their sport.
There's only two arguments. You've concocted the rest.
1. Symbolism
The name of the the governing body was changed in 2006 as a clean break from the past of the sport. That it coincided with the A-League's establishment and the 2006 WC also contributed to this symbolism. It sought to break from an era when the sport was derogatorily considered as being just for "Sheilas, W0gs, and twinkies".
It is a shame you have not evolved from that era. Your constant use of "soccer" reveals your desire to continue to see it as the marginalised sport of pre-2005.
2. It's the official name of the sport.
The FOOTBALL Federation of Australia is a member of the Asian FOOTBALL Confederation and the Fédération Internationale de FOOTBALL Association.
I haven't concocted anything - I'm telling you what soccer fans harp on about to me whenever they hear the word "soccer". Maybe the official line is different, but you'd by lying if you said you'd never heard some soccer douche crap on about how "it's played with the feet so it's football not soccer!!"
As for what the "official" name is, as I said before, it's actually "Association Football" - what you've provided is the renamed national body of Australia and some corrupt mafia crowd. In other countries - such as Japan for instance - the national body is the 日本サッカー協会 or Japan Soccer Association.
