had to laugh when I was told I wasn't a real Phoenix (and even football) fan, just because I chose to watch NZ play in cricket world cup final last season instead of going to a regular season nix game.
Some people just use the term 'fan' to give themselves a feeling of superiority (and greater sense of entitlement) over others.
It really is an arbitrary term. If you say you're a fan, you're a fan - whether you're a fickle fan or one who goes to every home game and pay the team $1 per win.