If anyone could explain a better intuition for this phrase, I would greatly appreciate it.
Consider the example from wikipedia:
Person 1: He is mad right now.
Person 2: How do you know?
Person 1: Well, because he is really angry.
If you think of it in terms of the meaning of beg as evade, then Person 1 is begging the inquiry of Person 2. She is evading it by restating the premise.