8/7k/7P/Rn5P/2B3p1/7P/1K1p1n2/8 w - - 0 1
Can You Find White's Drawing 1st Move?
The ultimate conclusion to this puzzle is inhuman, so reduce it to a drawn position confirmed by the Nalimov Tablebase.
Editor
7.Rxh3!?
Editor
1.Be2? gxh3
2.Ra4 d1=Q
3.Bxd1 Nxd1+
4.Kc1 Nf2
5.Rh4 Nd6
6.Kd2 Nf5
Editor
White can exchange the rook at h3 for the pawn. I know you probably already know that the ending is lost in that case, but it is the main line in 1.Be2, and why I mentioned the Nalimov Tablebase.
Bxe2 is a mistake because it allows to win a critical tempo for black.
1.Be2? gxh3
2.Ra4 d1=Q
3.Bxd1 Nxd1+
4.Kb3 Nf2
5.Rh4 Nd6
6.Kc3 Nf5
7.Rf4 h2
8.Rxf5 Ne4+
9.Kd3 h1=Q
It's a win for black.
Editor
Now explain why 1.Be2 fails to draw.