Add and Remove Button Listener not quite working

I have this game that I’ve made for my website http://www.roomrecess.com called Missile Mania (it’s a game for elementary kids, don’t laugh too hard…) Anyway, when you click on the start button, and the start button’s listener is removed, the in-game missile is fired right as you begin, even though I have not activated it’s listener yet. Is there a way to prevent this missile form firing until you click a second time (after you’ve clicked the start button)? The code is much too long to paste, but here is the address for the game, take a look: www.roomrecess.com/pages/MissileMania.html
Thanks!