A frequently-misused phrase is, "that begs the question," as though it means, "that fact or assertion leads to and demands the following line of inquiry." This is incorrect.
"Begging the question" means making a logical argument that uses its intended conclusion as part of its premise. The Latin name for this informal fallacy is petitio principii, and this roughly translates to, "an assumption from the beginning." It is a form of circular reasoning.
Ancient Aliens is chronically guilty of both misusing this term and employing the fallacy to which it refers. Their "evidence" for ancient alien intervention in human history is built on the premise that ancient alien theory is true in the first place. This circular reasoning is prevalent throughout the show's embarrasingly silly run. There are no efforts to falsify this premise through serious analysis. Their conclusions are not tested through examination of any alternative explanations or contradictory facts. No one employs properly skeptical inquiries into the various assertions made. It's always, "ancient alien theory is true because we explain these anomolies with ancient aliens."
As for incorrect usage of the phrase, an example is only about two and a half minutes into the first episode of season 14.* In response to recent strange scientific data, host and living meme Giorgio Tsoukalos says, "So the fact that cosmic rays were measured coming out of the Earth begs the question, how is such a thing possible?" His answer is, as always,
Sure, the anomalous measurement of strange radiation is worthy of investigation, and it raises questions as we seek an explanation, but it doesn't beg the question.
Hopefully this helps you avoid both the fallacy and the common linguistic error of begging the question. As always, comments are welcome below. Just keep it relevant, please.
*assuming this video upload isn't DMCA'd before you see this post