Know when (not) to resign

First, a little background.

My cousin taught me chess when I was a teenager.  I never really had anyone to play aginst and the lessons were mostly "the pieces move this way, now lets play".  In fact I don't ever remembering learning about material and values until I started (re-)learning chess later on in life.

Part of my re-education is utilizing the training positions in the Chess.com iOS app.  I will load up a position and play it over and over until I can 'see' the whys and hows, rather than just repeating a pattern.

I came across my first stumbling block: the 2 Bishop Mate position.  Everytime I think I understand then I get myself trapped in either a 3-fold repition draw or one of my bishops getting taken.  This is mostly to me not slowing down and just thinking 'hey I got this' and making moves without thinking them through.

While studing this problem I was playing the position aginst Stockfish on my PC and aligned my bishops and kings in the center and got the most unexpected (at the time) message: Stockfish has resigned.

My immediate response was "I am not sure I would be doing that if I were you." as I was not confident that I could execute the mate successfully.

This lead me to my unexpected lesson: Know when to NOT resign.  Stockfish assumed that I would execute the mate eventually (as it would) and just resigned.  In effect it overestimated me.  Certainly because you see an eventual end pause before throwing in the towel.

I can also see benifits for teachers not just resigning, leaving the student to wonder exactly how and why; allow the student to successfully execute the position.  Perhaps make a note of the 'turning point' in which you might have normally resigned and let them play it out, so you can reset when/if needed.  Or show them, I knew you had beat me at move XYZ.

It may be obvious if your oppant is of the skill level and you know that they will execute successfully.  In that case there is really no point in prolonging the enevitable, in fact admitting an early eventual defeat can say alot about your character. 

While I would rather win on skill, drawing on an oponents blunder is certainly acceptable.