Can You Find White's Drawing 1st Move?

7.Rxh3!?

1.Be2? gxh3
2.Ra4 d1=Q
3.Bxd1 Nxd1+
4.Kc1 Nf2
5.Rh4 Nd6
6.Kd2 Nf5

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.

Now explain why 1.Be2 fails to draw.