In conversation, the best way I've found to avoid causing frustration by the Socratic method is flattery. Every once in a while say "Ah yes", or "That's a valuable way to look at some problems", "I see where you're coming from", etc. And smiling and nodding irregularly when they say something less wrong than other statements. Sometimes, act as if the idea is new to you. Other times, attribute it knowingly to someone ostensibly respectable. It just takes a bit of positive feedback to keep a person to speak his or her mind.

A great way to get an arrogant person to reconsider an idea is to emphasize the priors they have right, have them work out inconsistencies with your simple, crafted questions, and then promote it as their idea, with a little bit of help that you provided.

It's not just questions instead of statements, it's a (partial) pretense of humbleness, an appeal to their ego to let you in. That's where I suspect people usually go wrong.