After hearing it used, I was looking up the correct usage of the term 'begs the question', because I heard somewhere that most people use it incorrectly, and came across this helpful page from Merriam Webster.

This bit at the end made me laugh out loud.

So that's where beg the question comes from, but all this, ahem, begs the question of what you should do with all this knowledge about the phrase. Liberman recommends that people avoid it altogether (but also "cultivate an attitude of serene detachment in the face of its use by others").

This is a major pet peeve of mine.

It doesn't mean it makes you want to ask a question!

a fact or an observation or a conclusion doesn't "beg the question," though one might enthymemetically imply a question that way. A person "begs [not to have to answer] the question" they were asked.

It does when people use it that way.