Under what circumstances would you NOT want a clean and minimalist website design?

I'm currently taking a web design/web development course and the two following questions are being touted as being extremely difficult by the course instructor, and I'm not too sure how to answer them:

  1. Under what circumstances would you NOT want a clean, sleek and minimalist website design?

  2. On the contrary, under what circumstances would you want a clean, sleek and minimalist design?

These questions take the stance of "you" being the web designer/web developer, but the instructor said that extremely good answers will consider both the perspective of the web developer AND the perspective of a user.