Suitability with Agile
Even if the external world didn't change during the life cycle of a Waterfall development process, the chances of giving stakeholders exactly what they expected are slim. This is especially true in Web development where subtle requirements such as user interface and navigation are difficult to describe without "trying them." Most stakeholders couldn't describe what they would like to see in these areas (especially for a new product) but they can tell you what they like and don't like. Even if stakeholders could tell you what they wanted it would be difficult to document. Undoubtedly, with enough time and money even these subtleties could be documented. But very few companies can afford the time and expense to do so.
These issues don't disappear with Agile methodologies, but they are decomposed to digestible pieces and code is evaluated early by stakeholders, modified based on their feedback, and built incrementally, so surprises are minimized. Further, the stakeholders also get a chance to refine their description of what they "really" want, once they begin to see how what they asked for actually works.
