Final answer:
The method that does not establish ethos is avoiding stating the opposing position to your argument, as it undermines the writer's credibility by suggesting a lack of awareness or consideration of alternative views.
Step-by-step explanation:
The question poses which method does not establish ethos. Ethos refers to the ethical appeal and is a way of convincing your audience of your credibility as a writer. Some ways to establish ethos include mentioning related experience to the topic, organizing argument in a logical manner, and using reliable sources. However, the choice that does not help in establishing ethos is avoid stating the opposing position to your argument. This is because addressing the contrary perspectives can actually strengthen ethos by showing the audience that you have considered and respected other points of view, and you are presenting an informed and balanced argument. Not addressing the opposition could lead the audience to believe that you are not aware of or are dismissing other valid viewpoints, which can undermine your credibility.