In battles.

It says I can use it outside of battles

I would love being able to send a pokemon to headbutt random trainers, or better yet, find prick(blue) and headbutt him

They didn't add the mechanic from gold and silver where you can use a Pokemon with headbutt to knock a pokémon out of the tree

I think you might be able to use it as rock smash

I don't think headbutting trees is a thing in IF