Just to add, Inverse Battles is just a small little battle feature that is only accessible on Route 18 with the Psychic dude in the house. He's the only place you can battle inversely, however he does have different Pokemon everyday, to my knowledge.
Out of all due respect, having a Wi-Fi inverse battle option is pretty redundant. I don't understand why, but it's just different to all the other types of battles. Except for Rotation Battles though - I hate them. The only feature to them is that you can switch Pokemon without taking a turn. Advantageous, yet redundant.
Sorry, just ranting.
Hope I helped. :)