There's really very little reason to ever use that expression. It's not a particularly good translation of petitio principii, which is itself not a good translation of a previous text. The Latin is a less ambiguous way to refer to the logical concept, and "begets" or "provokes" similarly avoids confusion with the common sense. That said, I do think you might be right about which they wanted.
As far as I can tell begets is the original form, begs is a mondegreen. I am using this deliberately only since I came across [1], to say "escapes the question". Alas that's just an unsubstantiated hunch. Maybe I should just write "escapes".
... which is akin to Latin fugio, fugere -- to flee. The analysis of OE begietan as be+get strikes me as faux-etymology fashioned after behold and the like, where beholden has little to do with holding, all the same.
This is a hobby of mine to the point of becoming neurotic. It's all in vein if a play of words needs explaining. It's still kind of insightful, if you'll entertain me a little longer.
If bʰegʷ- means to run, flee, then how is bʰeg-, to break, related? Why is to break rather reconstructed as bʰreg-. Why is bʰegʷ- given an alternative form bʰewg-? Does preḱ-, to ask, fit in here; or prey- or what it was with a related meaning? Maybe wreg-, whence wreck?
What about bag, pray, pay, fag, vag, way, weigh, etc etc.
Maybe to break away from always meant ''departure'', ''to go, run away''. Why are hurried news breaking? Why does German have "brandaktuell" instead, burning news? I have to break it to you, I don't know. I can already hear you begging the question to stop. But I have one more. Is a beggar someone living out of bags? I really don't want to know.
