Cooking with sourdough starter
The instructions should read to throw away half the starter if you haven't used it to make bread (i.e. the starter needs to be refreshed in order to continue living). If it doesn't get new flour and water, it has nothing to keep it alive. So it tells you to get rid of half (by baking or, at worst, chucking it out). You could keep it, but you would end up with a hell of a lot of starter (exponentially!).

As for food safety, I don't think you have much to worry about... However I'm sure some of the other food scientists on this site will regurgitate a bunch of stats for you soon...