Why not?
Playing against patzers
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No i wouldn't resign. The pain of missing the obvious will be enough for him/her to remember it in future. Besides who likes charity given to them in chess anyway? not many if they actually want more then the points. I would rather know i deserved the win then someone pointing out how i could of won and then resigned. In there shoes i would say no thanks if i didn't see it i deserved to lose!
P.S. In a mentoring game perhaps unrated your there to learn from them, so its a different environment, but in an actual game i would much rather win honestly if possible.
Hey, Hey! Careful what you say about Patzers! 
Everybody is a Patzer.
Resigning because your opponent missed an obvious mate? Plain silly! you play what's on the board, not what might have been.
Beating the tar out of a guy who missed mate in one against you? Right and proper! it's the only way he will learn.
I wouldn't resign. Trying to win at all costs is the only thing you're obliged to do.
If your chess skills aren't great, it doesn't mean you can't take a beating.
I'd be annoyed if I had the chance to play a great player and he didn't kick my ass because I missed something.
I wouldn't resign, but when playing against much weaker opponents, I usually show them that I can checkmate them, so that they take-back the move and play another one. This way more games don't end too quickly and some do come to an endgame. But it has happened before that I told them to take-back the move and then found out that every other move they make still leads to checkmate (big material advantage and nice piece placement gives many possibilities).
I always miss those moves that kasparov or Fischer would have never missed even when they were 10 years old. Should my opponent resign on those Occassions?
Patzers rule. 
everyone is a patzer until they break the 2000 rating barrier, after that you become an expert, than a master, than a grandmaster, and than you go crazy.
Before anyone goes off and says "you're a patzer yourself! you're so low-rated!" let me just say letting your little 7-year old brother use your account doesn't exactly help your rating.
Lets say you find someone at Borders to play chess with, and right after 1 game you realize he/she is a patzer. If you KNOW you're playing someone you can easily beat you just move the first piece that you see as a passable move until... By chance, the patzer has found himself in an equal position! Not only that, you blundered! But then the patzer plays the wrong move, throwing away the mate he had in 1 move. You then see you have mate in 5, but you are faced with this decision: Do you mate in a few combinative moves? Leaving the patzer amazed? Or do you reset the pieces, show the Patzer the mate he had, and properly resign? I know what you're thinking "well, he blundered, i'd mate him, blundering's a part of chess" but its not exactly what i did, i found myself in this position
Now, he would've mated easily with Qb7, but played Rc1?? I then showed him the mate I had but also, before he shook my hand, I resigned, showing him the mate he had. Have you found yourself doing this? By the way, the position above may not be correct, so dont tell me I was incorrect.