Some interesting biographical stuff here, but I can't accept the truth of this sentence. First of all, there are almost no logical arguments in Atlas Shrugged at all. There are merely flamboyant rhetorical speeches about how wonderful logic and reason are. What she says about logic and reasoning in those speeches is usually flagrantly false. What she calls the principle of either-or, for example, is the fallacy of false dichotomy. Secondly, even if her logic was valid, you can always reject a logically valid argument by refuting the truth of its premises. If you want to learn something about how logic actually works, you could check out this series of articles.