Probably because it's far easier to forbid something outright than to teach when it works well and when it doesn't. You don't need to eliminate adverbs. You should question how useful each one is.
Always aim to use the best word in the best sentence. If that best word is an adverb, use it.
As with so many elements within our chosen genres, questioning what we put into the prose is one of those constantly recurring themes with which we must deal. Whether it be a conlang, exposition about the world you've spent so much time building, exotic names, or, as in this case, the very words we use to express all of these ideas, moderation and justification walk hand in hand to determine how a scene ultimately is built.
I think when it comes right down to it, you have to look at a majority of what you've put in to a section and justify the existence, either of the information or the method of expression. With something as heavy as a conlang, for example, the best advice I've seen is to start with a reasonable number of words to be included (being none), and fight tooth and nail to justify ANY number beyond that initial figure. Alternately, when addressing something like the presence of adverbs (or any other decorative, expressive addition to your basic sentence structure), you're looking at the process of determining the very best way to communicate with the reader. Knowing not just what the scene looks like, feels like, smells like, but what you want the reader to get out of it will help simple up the decision as to which approaches might be most appropriate for that communication.
All of this is the concern of the writer in the editing process, though. First drafts don't have to adhere to the same lines of thought. If you want the character to shout something breathlessly, let him shout it breathlessly. If nothing else, it reminds YOU what feeling the action should convey. Going back over it, you can then take the time to determine if "breathlessly" is the very best way to express the idea, or if a restructuring of the sentence could create a more complete picture in the reader's mind.