Every once in a while, we do get questions where "that's not possible" is a valid answer to the question as asked (with perhaps further clarification in comments). Sometimes the question gives criteria that are mutually exclusive in some manner, and sometimes the asker is asking for a science-based (or maybe even hard-science!) method for doing something that science says is not possible.
In my opinion, to those questions, an answer that says effectively "it's not possible, and here's why" is useful and a perfectly valid answer. I have at least two such answers on my account on Worldbuilding, to Science-based FTL drive and to What would happen if electricity stopped working? respectively. (My answer to the former is currently accepted and highest voted, and my answer to the latter is currently the highest voted.)
However, we also have a tradition on Worldbuilding to take what's stated in the question as The Truth (tm), and to work within that when proposing answers. The idea behind that, of course, is that the poster knows their world best and is (hopefully) trying to solve some small issue within that world while maintaining consistency.
In what situations is a sufficiently explained "that's not possible" an appropriate answer to a question?
Feel free to break your answer up (or even post several answers, one for each case) for questions tagged reality-check, science-based and hard-science respectively, but if your answer doesn't apply equally well to all cases, make sure to explain in your answer which cases you are considering.