This question assumes too much. Not all people who are influenced by the media have eating disorders. In fact, I would argue that most people in media do not have eating disorders.
With that stated, some, undoubtedly, do have disorders. There are a number of possible reasons. First, often times the media portrays a certain type of beauty or more specifically a certain body shape as an ideal. Unfortunately, this ideal is far from attainable for most people. So, when people try to reach this ideal, there can have issues with eating disorders.
Second, the media has a way of changing our categories of thought and the way we perceive the world. For this reason, we might have a distorted view of the world and our bodies. This, too, can lead to various body issues and eating disorders.