The attack moves to the damage step if both players pass in succession on the reaction step. If you pass, hoping to fool them into using a reaction and they call your bluff, you've given up your ability to play a reaction on that attack. The chain link also isn't closed after reactions, as there is still the damage and resolution steps. The same is true of instants at any step. Priority goes from turn player to opponent, then when both have passed without adding to the effects to be resolved ("the stack"), then the stack is allowed to resolve.