9...Ne5 threatens to win a piece with 10...b5 11 Bb3 c5 12 ...c4
So white then must defend 10 Bb3 c5 11 Nf3 Nxf3+ 12 gxf3 with advantage for black
9...d6 is not that bad, but it is even after that. So 9...d6 is a missed win.
Why only this move is good?
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In this position, why Nc6 to Ne5 is the only good move for black? Is it because black will end up with doubled pawn after the exchange? And why is black position better than white after Ne5?