I agree that it can give insight into the reactions of others which can be valuable, but I think the disturbing idea is that someone could think it tells you anything about the internal experience of being someone with a legitimate stutter. It's human nature to want to empathize with others and important to relate as far as possible, but saying "I stutter on purpose sometimes, so I know how you feel when you stutter without wanting to" is insulting and invalidating, in my opinion. I still think it's a worthwhile assignment because of the reason you mentioned and what I said in my other comment, but OP's professor should be very careful about how she frames its purpose.