The phrase “begs the question” does not mean “raises the question.” “Beg the question” means “engage in circular reasoning” (within a single syllogism), or, more precisely, “assume the truth of the proposition you purport to be proving.”
For example, the fact that the phrase is so frequently misused does not beg the question of how our culture’s knowledge of the language we all supposedly speak has gone down the crapper.
Though it does raise it.