White doesn't have checkmate in 3. If he moves his knight and puts black in check then whites king can still find cover from the rook behind the knight. Giving him a chance to use the last row up.
Sounds like you've been playing easy beginners your whole life.
Solution:
(White) Ng4+ (Black)hxg4
(White)Bg8 (Black)Kh5 (Any move from Black is insufficient to prevent checkmate)
(White)Rh7#
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