Ozone is destroyed primarily by chlorine and bromine. Chlorine commonly exists in our world as dichlorine, or Cl2. The Chlorine that depletes ozone is a single atom, not the molecule Cl2. In order for this to happen, the Cl2 has to be split apart, and the way this happens in the Stratosphere is by photodissociation. Basically, the light from the sun is so energetic, that it breaks the molecule up into its elemental parts. But where does this chlorine come from in the first place?
Well, first, chlorine natuarally exists in the atmosphere. In fact, one of the causes (although by no means the predominant cause) of depletion of ozone are a phenomena called polar stratospheric clouds. These are clouds that actually exist in the stratosphere. How novel. But they aren’t clouds as you or I tend to think of clouds. These clouds are made up of water and nitric acid. Here’s a picture a woman gave me when I was down in Antarctica: Nacreous pretty, huh? Well, these clouds form activated chlorine (the single element, not Cl2), and we measured a few of these clouds this year because they give us a good sense of what kind of depletion is going on up there. But, they don’t last very long. Because they can only form at temperatures less than -80 degrees C, once the sun comes up in Antarctica, the stratosphere warms, and these clouds can’t form any more. Thus, reducing the ozone depletion.
The reason we see such a massive hole in the ozone layer is because of chloroflourocarbons, as I’m sure you’ve all heard of. These are emitted at the surface, and make it up to the stratosphere by upward moving air (think of a thunderstorm. This one storm has strong up drafts, and can deposit the CFCs into the stratosphere.) CFCs are not very reactive on their own, that’s why they can make it up that high. But remember photodissociation? Well, as soon as those bad boys get into the stratosphere, they dissociate and single Cl is free to roam around the atmosphere destroying ozone. And the big problem is that one Cl atom can destroy more than one molecule of ozone. Jerks.
So enough of my back history: to answer your question, I wouldn’t worry about space shuttles destroying ozone. It takes very specific elements to destroy ozone, and I am fairly certain the space agencies don’t use freon or halons (CFCs) to propel their spacecrafts.