I have a vague memory (as most of them are. these days!) that this was discussed about a year ago, and that it was established that "begging", in this context, was an archaic word for "avoiding."

So, in begging the question, you *avoid asking a question which ought to be addressed and then take your answer to it as given, when constructing an argument for or against something or other, trying to leave others with no choice but to accept your premisses.

(a device beloved of politicians!)