This is the Socratic method of arguing. It can also be as a Dark Side technique by choosing your questions so as to lead your counterpart into a trap - that their position is logically inconsistent, or implies that they have to bite a bullet that they don't want to admit to biting.

I've seen this "countered" by people simply refusing to talk any more, by repeating their original statement, or saying "No, that's not it" followed by something that seems incomprehensible.