How human beings treat one another is practically the definition of a public moral matter. Of course, there are many private aspects of human relations, but the question whether one human being should be allowed fatally to harm another is not one of them.
Abortion is an inescapably public matter.
Moreover, if the premisses of an instance of Begging the Question happen to be true, then the argument is sound . First of all, not all circular reasoning is fallacious . Then we have clearly argued in a circle, but this is a standard form of argument in mathematics to show that a set of propositions are all equivalent to each other. For an argument to have any epistemological or dialectical force, it must start from premisses already known or believed by its audience, and proceed to infer a conclusion not known or believed. This, of course, rules out the worst cases of Begging the Question, when the conclusion is the very same proposition as the premiss, since one cannot both believe and not believe the same thing.