I understand it allows the person to avoid answering a potentially uncomfortable or incriminating question directly.
Something to hide?
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Why do you ask?
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Who does something like that ?
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What sort of question?
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What?
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Spose it depends who’s asking the question, and, if they have the right to ask it in the first place 
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There’s very rarely something that I “always” do.
As for your question, yes, I occasionally do that for the reason you give, but more often in order to make the other one aware of something and to give them food for thought. Some people opine that answering a question with a question is rude. I don’t since such a first-mover advantage could hardly be justified.
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I answer the question and then I’m fairly likely to ask a question if the askers question was questionable.
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And how do you feel about that?
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If it makes me wonder why they are asking, then I reply with something like “Funny you should ask me that question. Exactly what I was going to ask you.”
Then, simply smile and wait for their response.
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“Who wants to know?” That’s a good question answering question to make the questioner feel uncomfortable.
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As is “WTF has it got to do with you?”
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I normally don’t take questions from random people… 
Tell them Nothing!
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Did you know there are 21 dots on a dice?
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Don’t tell him Pike
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That was a great episode.
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I never knew that Geli… 
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