An editor is a leader and manager of people and must therefore show sound judgment of character as well as diplomacy.
A sensitive person will require patience and compassion in conjunction with firmness. This kind of person is best led through a combination of consent and firmness.
Explain your understanding of the underlying principle of how you should lead this kind of person. Then talk about what actions you would take, bearing in mind that there are always deadlines to meet.
"A lot of writers are sensitive, which is understandable because they often put their heart and soul into it and they're doing the very best that they can. As an editor, I might be making tiny little edits on grammar and punctuation, which the writer might see as a slight. So I need to acknowledge their good work and the efforts they make. I might not have time to talk about every little edit, so I'll ask them to write down all their concerns so that we can have a meeting where we can talk about the newspaper's expectations and guidelines. That way we can meet the deadline and the writer still gets to be heard and understood."