the FA - "Football Association".
Australian Rules deserves to be called "football" in Australia as it was the first football code played here. Who cares what they call it overseas. No different to what happens in the USA with the NFL and soccer.
It would be 500 years, if at all, before it would be called 'football' in Sydney.
'soccer', league and union all have prior claims to the title here. It's 'aussie rules' in Sydney.