"Wrong question" is a short-hand way to respond to a question that cannot be answered directly because it contains a logical fallacy, incorrect assumption, or heads in a completely wrong direction. The canonical example of a wrong question is, "When did you stop beating your wife?" because it presumes that you were at one point beating your wife (maybe you never had a wife, maybe you never beat her).
It can be difficult to figure out how to respond to a wrong question. Usually they're just mis-phrasings or mis-thinkings, but consider the case of visiting a car dealer and saying that you don't think a car meets your needs. If the salescritter says, "What's wrong with silver?" that's a deliberate use of a wrong question designed to scramble your thinking.
It can be even more difficult to figure out how to respond to an innocent wrong question because often the wrong question elicits an emotional response of violation; if it's an innocent wrong question, you don't really want to bark back at the person. At the same time, wrong questions are so prevalent that I generally choose the course of responding directly back because I believe that they are harmful to considered discourse.
For example, the question that sparked this essay: "why would you not want to be kind to people?" It assumes that I don't want to be kind (i.e., lacking in desire to be kind) rather than choosing to be less than kind for other reasons. I found that particularly annoying because it was responding to a comment I made where I said that I didn't know whether it was worth the effort to be kind -- I said nothing about not wanting to be kind.