I think you should define it by what it really is, to someone just starting out a basic definition will be more valueable to them, leaving them to discover there own reasons for doing it. Defining your reasons for doing it, isn't really a definition of the sport, now is it, .
To each of us the definition of fly fishing should basically be the same, just like how baseball and hockey is fundamentally the same game to each of the baseball or hockey players on a team, although they all have different styles, means and reasons for doing it, in the end the game is the game.

Heres how I would go about it.
I would state that fly fishing is exactly what the name implies, fishing with flies. Then I would go on to state how we go about it and how it works covering different aspects of the sport like you have suggested, maybe during some part of the course you could offer your reasons for doing it but not until they have the basics.

later
Mike

[This message has been edited by Newfoundlander (edited 26 January 2006).]