It is a common suggestion but I think it would be a mistake to require people to post reasons for their downvotes. It would produce a ton of noise (because people would just make shit up) and dramatically increase meta-bickering about downvotes, which we already have too much of.

Edit: here's a partial list of past explanations about this, in case anyone is interested in seeing how it has come up over the years: https://news.ycombinator.com/downvote-reasons