The problem is the Socratic Method should only be used on someone who accepts that you're trying to teach them something. It's insulting when used in another context.
Strictly speaking, I think you're right, but many people use the phrase Socratic Method to mean any interaction in which you use questions to influence someone's thinking.
Feigning ignorance (or playing dumb) can be an extremely effective tactic in this area. Start with a simple question that is almost embarrassingly simple and then angle follow-ups towards the actual problem/inconsistency/concern/whatever. You often don't even need to ask follow-up questions; overly simple questions get people thinking about their core assumptions, which is often the root of the problem. Or their answer reveals flawed core assumptions, which is equally good.
I agree, but people quickly figure out you're trying to manipulate them and they still get angry. It's pretty rare that someone changes their mind based on your questioning their assumptions even if feigning ignorance.
