This is the best explanation of the reasoning behind “it’s not my job to teach you” that I’ve seen.
I’ve usually come across it in angry or condescending conversations (and rightfully so, in my opinion) when people aren’t at their best. It’s nice to see a response that’s unemotional yet sincere.
In this case, I think your interpretation (“I’m just gonna disengage while trying to save face”) is spot on.
I can see it going the other way, though. I might finally respond with “figure it out for yourself” after a sealioning pedant has exhausted me, and I would rather end the conversation than explain my point for the third or fourth time.