Burke the question
To burke a question is to smother it - that is, to avoid answering by simply ignoring it. The expression is a figurative use of the name of a famous Edinburgh murderer, William Burke (1792-1829), who with his accomplice William Hare, used to sell corpses to the medical schools for dissection. They used to produce the bodies for this purpose with no mark of murder on them, having used suffocation.
This may be a better expression for the meaning that is sometimes erroneously written as beg the question.