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Why is this the correct answer to chesspuzzle.net puzzle 37161?

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https://chesspuzzle.net/Puzzle/37161

[FEN "r4rk1/2p2n1q/1p1b4/3Pp3/2Q2pP1/P1N1B2P/1P4P1/2RR2K1 w - - 0 1"]1. Ne4 

The answer given is Ne4, which is followed by the pawn on f4 capturing the bishop on e3, at which point white is able to fork black's king and queen, however this is entirely avoidable by black simply moving either the king or queen to a square that prevents the fork from happening, e.g. Qh6. So why is Ne4 a better solution to this puzzle than simply moving the bishop to a safe square, e.g. d2?


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