Everyman is a relatively unique monster in that it can't be hurt during its turn. This means any attacking that it does will not result in damage to Everyman. This also means that cards who have an ability that triggers when a monster is damaged by it, such as Ice, will not have their effect take place.
Keep in mind that this does not work whilst defending, unlike with cards such as Mad Dummy and Sans. As such, it's good to use this alongside one or two monsters with Taunt.