What would be the reasons to design a website with Flash instead of static HTML?

With Flash, you are allowed more liberties on the visual and interactive aspects of a website's design. With Flash, it is possible to incorporate sound and animation in a website experience in a more elegant manner. For HTML, it is possible to have sound and animation, but these would be seperate files put into the website, and they would not be as integrated in the design as it could be for Flash. Also, Flash is more versatile in what it can do. A website can be constructed almost to play like an interactive expereince, or a game, or an animation, as opposed to a static website.

Why would you choose to use PHP (or other dynamically-generated page technology) instead of HTML?

PHP is far more dynamic than static HTML. Because of its ability to group and sort pieces of information according to its code, it is super useful for fast and dynamic updates of a website. This can occur in a nearly automatic manner. This contrasts statuc html's need for a complete update from the user. In other words, the user would need to do all of the work involved with updating a website. This also means it is great for forums, which could be viewd as a dynamic website that is constantly updating. It is also useful for search functions and a variety of other data managment tasks that static html simply cannot do.