ebo, your Mimi example is a good one. However, you did not tell me, who Mimi is to you.
If Mimi is your daughter, I would say, you do need to ask her why. Unless you know what motivated her, or what she intended to accomplish, you cannot help her sort out her error.
If Mimi is one of your students you might want to help her sort things out, the way you might do for your own child (spouse, close friend, etc.).
However, if Mimi is an acquaintance, or a stranger, you have no right to her motivations and intentions. Motivations, intentions and beliefs are personal, even private matters, and people should respect, not cross personal boundaries. When people know and trust us, they will confide in us, and share their real motivations, intentions, and beliefs, without being asked.
Your Kate example is another good one. It sounds like Kate is a stranger, who was attending the same lecture as you. A good lecturer should have cleared things up. If not, ask the lecturer to explain the significance of the question – not Kate. Given Kate’s question, it seems rather likely that the lecturer handled a loaded question rather well.
Who, what, when, where and how questions are more powerful than why. Mimi, what did you just say, I want to hear you repeat it. Mimi, where did you hear that word? Mimi, when was the first time you heard someone use that word and who said it? Mimi, how do you think people would, or should respond to that word? Asking Mimi why she said it, invites an endless stream of meaningless babble. It sounds like Mimi needs a therapist, a teacher, or an adult, not an audience.
Those are my thoughts.