Just to add another point to all of this: evidence suggests that the very act of believing in innate ability actually lowers your ability overall, even if you believe you are innately talented. So just the fact that so many advisors believe this is undoubtedly unnecessarily discouraging to many students. It is unacceptable to express this view to students, even if you believe it is true.

@WilliamOliver: That's in the basket of pop-priming studies in psychology/education that have failed a bunch of large-scale replication attempts.

@DanielR.Collins Interesting. Well, hopefully my fopaux in mentioning a study which hasn't had many successful replication attempts does not detract from the point, that an advisor should not make assumptions about whether a student has innate ability or not. It is unclear whether either view is harmful, so it's best to focus on only the matter at hand, and avoid attempting to predict the entire trajectory of a student's life.

But for someone else it could be rough to hear. That said, I can imagine if the student has missed deadline after deadline and in exasperation she's said something like this because the student just didn't get the picture, I can imagine that happening. And I can imagine some people thinking it's ok. I think it's a bit harsh but eh. Communication is hard sometimes.